Divisibility worksheet with numbers and a grid for checking divisibility.
Educational worksheet: Long Division Worksheet. Download and print for classroom or home learning activities.
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Show Answer Key & Explanations
Step-by-step solution for: Long Division Worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Long Division Worksheet
To solve this problem, we need to determine whether each number in the left column is divisible by the numbers at the top of each column. If a number is divisible, we write "Y" (YES); otherwise, we write "N" (NO).
1. Understand divisibility: A number \( A \) is divisible by \( B \) if \( A \div B \) results in an integer with no remainder.
2. Perform the division for each pair:
- For each row (number on the left), check divisibility by each column header (numbers 2 through 12).
- Use the modulus operator (\( \mod \)) to check if the remainder is zero.
#### Row: 87
- \( 87 \div 2 = 43.5 \) (remainder ≠ 0) → N
- \( 87 \div 3 = 29 \) (remainder = 0) → Y
- \( 87 \div 4 = 21.75 \) (remainder ≠ 0) → N
- \( 87 \div 5 = 17.4 \) (remainder ≠ 0) → N
- \( 87 \div 6 = 14.5 \) (remainder ≠ 0) → N
- \( 87 \div 7 = 12.4286 \) (remainder ≠ 0) → N
- \( 87 \div 8 = 10.875 \) (remainder ≠ 0) → N
- \( 87 \div 9 = 9.6667 \) (remainder ≠ 0) → N
- \( 87 \div 10 = 8.7 \) (remainder ≠ 0) → N
- \( 87 \div 11 = 7.9091 \) (remainder ≠ 0) → N
- \( 87 \div 12 = 7.25 \) (remainder ≠ 0) → N
#### Row: 42
- \( 42 \div 2 = 21 \) (remainder = 0) → Y
- \( 42 \div 3 = 14 \) (remainder = 0) → Y
- \( 42 \div 4 = 10.5 \) (remainder ≠ 0) → N
- \( 42 \div 5 = 8.4 \) (remainder ≠ 0) → N
- \( 42 \div 6 = 7 \) (remainder = 0) → Y
- \( 42 \div 7 = 6 \) (remainder = 0) → Y
- \( 42 \div 8 = 5.25 \) (remainder ≠ 0) → N
- \( 42 \div 9 = 4.6667 \) (remainder ≠ 0) → N
- \( 42 \div 10 = 4.2 \) (remainder ≠ 0) → N
- \( 42 \div 11 = 3.8182 \) (remainder ≠ 0) → N
- \( 42 \div 12 = 3.5 \) (remainder ≠ 0) → N
#### Row: 52
- \( 52 \div 2 = 26 \) (remainder = 0) → Y
- \( 52 \div 3 = 17.3333 \) (remainder ≠ 0) → N
- \( 52 \div 4 = 13 \) (remainder = 0) → Y
- \( 52 \div 5 = 10.4 \) (remainder ≠ 0) → N
- \( 52 \div 6 = 8.6667 \) (remainder ≠ 0) → N
- \( 52 \div 7 = 7.4286 \) (remainder ≠ 0) → N
- \( 52 \div 8 = 6.5 \) (remainder ≠ 0) → N
- \( 52 \div 9 = 5.7778 \) (remainder ≠ 0) → N
- \( 52 \div 10 = 5.2 \) (remainder ≠ 0) → N
- \( 52 \div 11 = 4.7273 \) (remainder ≠ 0) → N
- \( 52 \div 12 = 4.3333 \) (remainder ≠ 0) → N
#### Row: 96
- \( 96 \div 2 = 48 \) (remainder = 0) → Y
- \( 96 \div 3 = 32 \) (remainder = 0) → Y
- \( 96 \div 4 = 24 \) (remainder = 0) → Y
- \( 96 \div 5 = 19.2 \) (remainder ≠ 0) → N
- \( 96 \div 6 = 16 \) (remainder = 0) → Y
- \( 96 \div 7 = 13.7143 \) (remainder ≠ 0) → N
- \( 96 \div 8 = 12 \) (remainder = 0) → Y
- \( 96 \div 9 = 10.6667 \) (remainder ≠ 0) → N
- \( 96 \div 10 = 9.6 \) (remainder ≠ 0) → N
- \( 96 \div 11 = 8.7273 \) (remainder ≠ 0) → N
- \( 96 \div 12 = 8 \) (remainder = 0) → Y
#### Row: 74
- \( 74 \div 2 = 37 \) (remainder = 0) → Y
- \( 74 \div 3 = 24.6667 \) (remainder ≠ 0) → N
- \( 74 \div 4 = 18.5 \) (remainder ≠ 0) → N
- \( 74 \div 5 = 14.8 \) (remainder ≠ 0) → N
- \( 74 \div 6 = 12.3333 \) (remainder ≠ 0) → N
- \( 74 \div 7 = 10.5714 \) (remainder ≠ 0) → N
- \( 74 \div 8 = 9.25 \) (remainder ≠ 0) → N
- \( 74 \div 9 = 8.2222 \) (remainder ≠ 0) → N
- \( 74 \div 10 = 7.4 \) (remainder ≠ 0) → N
- \( 74 \div 11 = 6.7273 \) (remainder ≠ 0) → N
- \( 74 \div 12 = 6.1667 \) (remainder ≠ 0) → N
#### Row: 86
- \( 86 \div 2 = 43 \) (remainder = 0) → Y
- \( 86 \div 3 = 28.6667 \) (remainder ≠ 0) → N
- \( 86 \div 4 = 21.5 \) (remainder ≠ 0) → N
- \( 86 \div 5 = 17.2 \) (remainder ≠ 0) → N
- \( 86 \div 6 = 14.3333 \) (remainder ≠ 0) → N
- \( 86 \div 7 = 12.2857 \) (remainder ≠ 0) → N
- \( 86 \div 8 = 10.75 \) (remainder ≠ 0) → N
- \( 86 \div 9 = 9.5556 \) (remainder ≠ 0) → N
- \( 86 \div 10 = 8.6 \) (remainder ≠ 0) → N
- \( 86 \div 11 = 7.8182 \) (remainder ≠ 0) → N
- \( 86 \div 12 = 7.1667 \) (remainder ≠ 0) → N
#### Row: 48
- \( 48 \div 2 = 24 \) (remainder = 0) → Y
- \( 48 \div 3 = 16 \) (remainder = 0) → Y
- \( 48 \div 4 = 12 \) (remainder = 0) → Y
- \( 48 \div 5 = 9.6 \) (remainder ≠ 0) → N
- \( 48 \div 6 = 8 \) (remainder = 0) → Y
- \( 48 \div 7 = 6.8571 \) (remainder ≠ 0) → N
- \( 48 \div 8 = 6 \) (remainder = 0) → Y
- \( 48 \div 9 = 5.3333 \) (remainder ≠ 0) → N
- \( 48 \div 10 = 4.8 \) (remainder ≠ 0) → N
- \( 48 \div 11 = 4.3636 \) (remainder ≠ 0) → N
- \( 48 \div 12 = 4 \) (remainder = 0) → Y
#### Row: 24
- \( 24 \div 2 = 12 \) (remainder = 0) → Y
- \( 24 \div 3 = 8 \) (remainder = 0) → Y
- \( 24 \div 4 = 6 \) (remainder = 0) → Y
- \( 24 \div 5 = 4.8 \) (remainder ≠ 0) → N
- \( 24 \div 6 = 4 \) (remainder = 0) → Y
- \( 24 \div 7 = 3.4286 \) (remainder ≠ 0) → N
- \( 24 \div 8 = 3 \) (remainder = 0) → Y
- \( 24 \div 9 = 2.6667 \) (remainder ≠ 0) → N
- \( 24 \div 10 = 2.4 \) (remainder ≠ 0) → N
- \( 24 \div 11 = 2.1818 \) (remainder ≠ 0) → N
- \( 24 \div 12 = 2 \) (remainder = 0) → Y
#### Row: 33
- \( 33 \div 2 = 16.5 \) (remainder ≠ 0) → N
- \( 33 \div 3 = 11 \) (remainder = 0) → Y
- \( 33 \div 4 = 8.25 \) (remainder ≠ 0) → N
- \( 33 \div 5 = 6.6 \) (remainder ≠ 0) → N
- \( 33 \div 6 = 5.5 \) (remainder ≠ 0) → N
- \( 33 \div 7 = 4.7143 \) (remainder ≠ 0) → N
- \( 33 \div 8 = 4.125 \) (remainder ≠ 0) → N
- \( 33 \div 9 = 3.6667 \) (remainder ≠ 0) → N
- \( 33 \div 10 = 3.3 \) (remainder ≠ 0) → N
- \( 33 \div 11 = 3 \) (remainder = 0) → Y
- \( 33 \div 12 = 2.75 \) (remainder ≠ 0) → N
#### Row: 60
- \( 60 \div 2 = 30 \) (remainder = 0) → Y
- \( 60 \div 3 = 20 \) (remainder = 0) → Y
- \( 60 \div 4 = 15 \) (remainder = 0) → Y
- \( 60 \div 5 = 12 \) (remainder = 0) → Y
- \( 60 \div 6 = 10 \) (remainder = 0) → Y
- \( 60 \div 7 = 8.5714 \) (remainder ≠ 0) → N
- \( 60 \div 8 = 7.5 \) (remainder ≠ 0) → N
- \( 60 \div 9 = 6.6667 \) (remainder ≠ 0) → N
- \( 60 \div 10 = 6 \) (remainder = 0) → Y
- \( 60 \div 11 = 5.4545 \) (remainder ≠ 0) → N
- \( 60 \div 12 = 5 \) (remainder = 0) → Y
#### Row: 88
- \( 88 \div 2 = 44 \) (remainder = 0) → Y
- \( 88 \div 3 = 29.3333 \) (remainder ≠ 0) → N
- \( 88 \div 4 = 22 \) (remainder = 0) → Y
- \( 88 \div 5 = 17.6 \) (remainder ≠ 0) → N
- \( 88 \div 6 = 14.6667 \) (remainder ≠ 0) → N
- \( 88 \div 7 = 12.5714 \) (remainder ≠ 0) → N
- \( 88 \div 8 = 11 \) (remainder = 0) → Y
- \( 88 \div 9 = 9.7778 \) (remainder ≠ 0) → N
- \( 88 \div 10 = 8.8 \) (remainder ≠ 0) → N
- \( 88 \div 11 = 8 \) (remainder = 0) → Y
- \( 88 \div 12 = 7.3333 \) (remainder ≠ 0) → N
#### Row: 72
- \( 72 \div 2 = 36 \) (remainder = 0) → Y
- \( 72 \div 3 = 24 \) (remainder = 0) → Y
- \( 72 \div 4 = 18 \) (remainder = 0) → Y
- \( 72 \div 5 = 14.4 \) (remainder ≠ 0) → N
- \( 72 \div 6 = 12 \) (remainder = 0) → Y
- \( 72 \div 7 = 10.2857 \) (remainder ≠ 0) → N
- \( 72 \div 8 = 9 \) (remainder = 0) → Y
- \( 72 \div 9 = 8 \) (remainder = 0) → Y
- \( 72 \div 10 = 7.2 \) (remainder ≠ 0) → N
- \( 72 \div 11 = 6.5455 \) (remainder ≠ 0) → N
- \( 72 \div 12 = 6 \) (remainder = 0) → Y
\[
\boxed{
\begin{array}{c|ccccccccccc}
& 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\
\hline
87 & N & Y & N & N & N & N & N & N & N & N & N \\
42 & Y & Y & N & N & Y & Y & N & N & N & N & N \\
52 & Y & N & Y & N & N & N & N & N & N & N & N \\
96 & Y & Y & Y & N & Y & N & Y & N & N & N & Y \\
74 & Y & N & N & N & N & N & N & N & N & N & N \\
86 & Y & N & N & N & N & N & N & N & N & N & N \\
48 & Y & Y & Y & N & Y & N & Y & N & N & N & Y \\
24 & Y & Y & Y & N & Y & N & Y & N & N & N & Y \\
33 & N & Y & N & N & N & N & N & N & N & Y & N \\
60 & Y & Y & Y & Y & Y & N & N & N & Y & N & Y \\
88 & Y & N & Y & N & N & N & Y & N & N & Y & N \\
72 & Y & Y & Y & N & Y & N & Y & Y & N & N & Y \\
\end{array}
}
\]
Steps:
1. Understand divisibility: A number \( A \) is divisible by \( B \) if \( A \div B \) results in an integer with no remainder.
2. Perform the division for each pair:
- For each row (number on the left), check divisibility by each column header (numbers 2 through 12).
- Use the modulus operator (\( \mod \)) to check if the remainder is zero.
Solution:
#### Row: 87
- \( 87 \div 2 = 43.5 \) (remainder ≠ 0) → N
- \( 87 \div 3 = 29 \) (remainder = 0) → Y
- \( 87 \div 4 = 21.75 \) (remainder ≠ 0) → N
- \( 87 \div 5 = 17.4 \) (remainder ≠ 0) → N
- \( 87 \div 6 = 14.5 \) (remainder ≠ 0) → N
- \( 87 \div 7 = 12.4286 \) (remainder ≠ 0) → N
- \( 87 \div 8 = 10.875 \) (remainder ≠ 0) → N
- \( 87 \div 9 = 9.6667 \) (remainder ≠ 0) → N
- \( 87 \div 10 = 8.7 \) (remainder ≠ 0) → N
- \( 87 \div 11 = 7.9091 \) (remainder ≠ 0) → N
- \( 87 \div 12 = 7.25 \) (remainder ≠ 0) → N
#### Row: 42
- \( 42 \div 2 = 21 \) (remainder = 0) → Y
- \( 42 \div 3 = 14 \) (remainder = 0) → Y
- \( 42 \div 4 = 10.5 \) (remainder ≠ 0) → N
- \( 42 \div 5 = 8.4 \) (remainder ≠ 0) → N
- \( 42 \div 6 = 7 \) (remainder = 0) → Y
- \( 42 \div 7 = 6 \) (remainder = 0) → Y
- \( 42 \div 8 = 5.25 \) (remainder ≠ 0) → N
- \( 42 \div 9 = 4.6667 \) (remainder ≠ 0) → N
- \( 42 \div 10 = 4.2 \) (remainder ≠ 0) → N
- \( 42 \div 11 = 3.8182 \) (remainder ≠ 0) → N
- \( 42 \div 12 = 3.5 \) (remainder ≠ 0) → N
#### Row: 52
- \( 52 \div 2 = 26 \) (remainder = 0) → Y
- \( 52 \div 3 = 17.3333 \) (remainder ≠ 0) → N
- \( 52 \div 4 = 13 \) (remainder = 0) → Y
- \( 52 \div 5 = 10.4 \) (remainder ≠ 0) → N
- \( 52 \div 6 = 8.6667 \) (remainder ≠ 0) → N
- \( 52 \div 7 = 7.4286 \) (remainder ≠ 0) → N
- \( 52 \div 8 = 6.5 \) (remainder ≠ 0) → N
- \( 52 \div 9 = 5.7778 \) (remainder ≠ 0) → N
- \( 52 \div 10 = 5.2 \) (remainder ≠ 0) → N
- \( 52 \div 11 = 4.7273 \) (remainder ≠ 0) → N
- \( 52 \div 12 = 4.3333 \) (remainder ≠ 0) → N
#### Row: 96
- \( 96 \div 2 = 48 \) (remainder = 0) → Y
- \( 96 \div 3 = 32 \) (remainder = 0) → Y
- \( 96 \div 4 = 24 \) (remainder = 0) → Y
- \( 96 \div 5 = 19.2 \) (remainder ≠ 0) → N
- \( 96 \div 6 = 16 \) (remainder = 0) → Y
- \( 96 \div 7 = 13.7143 \) (remainder ≠ 0) → N
- \( 96 \div 8 = 12 \) (remainder = 0) → Y
- \( 96 \div 9 = 10.6667 \) (remainder ≠ 0) → N
- \( 96 \div 10 = 9.6 \) (remainder ≠ 0) → N
- \( 96 \div 11 = 8.7273 \) (remainder ≠ 0) → N
- \( 96 \div 12 = 8 \) (remainder = 0) → Y
#### Row: 74
- \( 74 \div 2 = 37 \) (remainder = 0) → Y
- \( 74 \div 3 = 24.6667 \) (remainder ≠ 0) → N
- \( 74 \div 4 = 18.5 \) (remainder ≠ 0) → N
- \( 74 \div 5 = 14.8 \) (remainder ≠ 0) → N
- \( 74 \div 6 = 12.3333 \) (remainder ≠ 0) → N
- \( 74 \div 7 = 10.5714 \) (remainder ≠ 0) → N
- \( 74 \div 8 = 9.25 \) (remainder ≠ 0) → N
- \( 74 \div 9 = 8.2222 \) (remainder ≠ 0) → N
- \( 74 \div 10 = 7.4 \) (remainder ≠ 0) → N
- \( 74 \div 11 = 6.7273 \) (remainder ≠ 0) → N
- \( 74 \div 12 = 6.1667 \) (remainder ≠ 0) → N
#### Row: 86
- \( 86 \div 2 = 43 \) (remainder = 0) → Y
- \( 86 \div 3 = 28.6667 \) (remainder ≠ 0) → N
- \( 86 \div 4 = 21.5 \) (remainder ≠ 0) → N
- \( 86 \div 5 = 17.2 \) (remainder ≠ 0) → N
- \( 86 \div 6 = 14.3333 \) (remainder ≠ 0) → N
- \( 86 \div 7 = 12.2857 \) (remainder ≠ 0) → N
- \( 86 \div 8 = 10.75 \) (remainder ≠ 0) → N
- \( 86 \div 9 = 9.5556 \) (remainder ≠ 0) → N
- \( 86 \div 10 = 8.6 \) (remainder ≠ 0) → N
- \( 86 \div 11 = 7.8182 \) (remainder ≠ 0) → N
- \( 86 \div 12 = 7.1667 \) (remainder ≠ 0) → N
#### Row: 48
- \( 48 \div 2 = 24 \) (remainder = 0) → Y
- \( 48 \div 3 = 16 \) (remainder = 0) → Y
- \( 48 \div 4 = 12 \) (remainder = 0) → Y
- \( 48 \div 5 = 9.6 \) (remainder ≠ 0) → N
- \( 48 \div 6 = 8 \) (remainder = 0) → Y
- \( 48 \div 7 = 6.8571 \) (remainder ≠ 0) → N
- \( 48 \div 8 = 6 \) (remainder = 0) → Y
- \( 48 \div 9 = 5.3333 \) (remainder ≠ 0) → N
- \( 48 \div 10 = 4.8 \) (remainder ≠ 0) → N
- \( 48 \div 11 = 4.3636 \) (remainder ≠ 0) → N
- \( 48 \div 12 = 4 \) (remainder = 0) → Y
#### Row: 24
- \( 24 \div 2 = 12 \) (remainder = 0) → Y
- \( 24 \div 3 = 8 \) (remainder = 0) → Y
- \( 24 \div 4 = 6 \) (remainder = 0) → Y
- \( 24 \div 5 = 4.8 \) (remainder ≠ 0) → N
- \( 24 \div 6 = 4 \) (remainder = 0) → Y
- \( 24 \div 7 = 3.4286 \) (remainder ≠ 0) → N
- \( 24 \div 8 = 3 \) (remainder = 0) → Y
- \( 24 \div 9 = 2.6667 \) (remainder ≠ 0) → N
- \( 24 \div 10 = 2.4 \) (remainder ≠ 0) → N
- \( 24 \div 11 = 2.1818 \) (remainder ≠ 0) → N
- \( 24 \div 12 = 2 \) (remainder = 0) → Y
#### Row: 33
- \( 33 \div 2 = 16.5 \) (remainder ≠ 0) → N
- \( 33 \div 3 = 11 \) (remainder = 0) → Y
- \( 33 \div 4 = 8.25 \) (remainder ≠ 0) → N
- \( 33 \div 5 = 6.6 \) (remainder ≠ 0) → N
- \( 33 \div 6 = 5.5 \) (remainder ≠ 0) → N
- \( 33 \div 7 = 4.7143 \) (remainder ≠ 0) → N
- \( 33 \div 8 = 4.125 \) (remainder ≠ 0) → N
- \( 33 \div 9 = 3.6667 \) (remainder ≠ 0) → N
- \( 33 \div 10 = 3.3 \) (remainder ≠ 0) → N
- \( 33 \div 11 = 3 \) (remainder = 0) → Y
- \( 33 \div 12 = 2.75 \) (remainder ≠ 0) → N
#### Row: 60
- \( 60 \div 2 = 30 \) (remainder = 0) → Y
- \( 60 \div 3 = 20 \) (remainder = 0) → Y
- \( 60 \div 4 = 15 \) (remainder = 0) → Y
- \( 60 \div 5 = 12 \) (remainder = 0) → Y
- \( 60 \div 6 = 10 \) (remainder = 0) → Y
- \( 60 \div 7 = 8.5714 \) (remainder ≠ 0) → N
- \( 60 \div 8 = 7.5 \) (remainder ≠ 0) → N
- \( 60 \div 9 = 6.6667 \) (remainder ≠ 0) → N
- \( 60 \div 10 = 6 \) (remainder = 0) → Y
- \( 60 \div 11 = 5.4545 \) (remainder ≠ 0) → N
- \( 60 \div 12 = 5 \) (remainder = 0) → Y
#### Row: 88
- \( 88 \div 2 = 44 \) (remainder = 0) → Y
- \( 88 \div 3 = 29.3333 \) (remainder ≠ 0) → N
- \( 88 \div 4 = 22 \) (remainder = 0) → Y
- \( 88 \div 5 = 17.6 \) (remainder ≠ 0) → N
- \( 88 \div 6 = 14.6667 \) (remainder ≠ 0) → N
- \( 88 \div 7 = 12.5714 \) (remainder ≠ 0) → N
- \( 88 \div 8 = 11 \) (remainder = 0) → Y
- \( 88 \div 9 = 9.7778 \) (remainder ≠ 0) → N
- \( 88 \div 10 = 8.8 \) (remainder ≠ 0) → N
- \( 88 \div 11 = 8 \) (remainder = 0) → Y
- \( 88 \div 12 = 7.3333 \) (remainder ≠ 0) → N
#### Row: 72
- \( 72 \div 2 = 36 \) (remainder = 0) → Y
- \( 72 \div 3 = 24 \) (remainder = 0) → Y
- \( 72 \div 4 = 18 \) (remainder = 0) → Y
- \( 72 \div 5 = 14.4 \) (remainder ≠ 0) → N
- \( 72 \div 6 = 12 \) (remainder = 0) → Y
- \( 72 \div 7 = 10.2857 \) (remainder ≠ 0) → N
- \( 72 \div 8 = 9 \) (remainder = 0) → Y
- \( 72 \div 9 = 8 \) (remainder = 0) → Y
- \( 72 \div 10 = 7.2 \) (remainder ≠ 0) → N
- \( 72 \div 11 = 6.5455 \) (remainder ≠ 0) → N
- \( 72 \div 12 = 6 \) (remainder = 0) → Y
Final Answer:
\[
\boxed{
\begin{array}{c|ccccccccccc}
& 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\
\hline
87 & N & Y & N & N & N & N & N & N & N & N & N \\
42 & Y & Y & N & N & Y & Y & N & N & N & N & N \\
52 & Y & N & Y & N & N & N & N & N & N & N & N \\
96 & Y & Y & Y & N & Y & N & Y & N & N & N & Y \\
74 & Y & N & N & N & N & N & N & N & N & N & N \\
86 & Y & N & N & N & N & N & N & N & N & N & N \\
48 & Y & Y & Y & N & Y & N & Y & N & N & N & Y \\
24 & Y & Y & Y & N & Y & N & Y & N & N & N & Y \\
33 & N & Y & N & N & N & N & N & N & N & Y & N \\
60 & Y & Y & Y & Y & Y & N & N & N & Y & N & Y \\
88 & Y & N & Y & N & N & N & Y & N & N & Y & N \\
72 & Y & Y & Y & N & Y & N & Y & Y & N & N & Y \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of math aids com division worksheets.
