Factors and Multiples - Worksheet Digital - Free Printable

Problem Explanation:

The task is to list the factors of specific numbers. Factors are numbers that divide another number exactly without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers divides 12 without any remainder.

Solution:

#### a) List the factors of 9
To find the factors of 9, we need to identify all the numbers that divide 9 exactly. We do this by checking divisibility from 1 up to 9.

- \( 9 \div 1 = 9 \) (remainder 0)
- \( 9 \div 2 = 4.5 \) (not divisible)
- \( 9 \div 3 = 3 \) (remainder 0)
- \( 9 \div 4 = 2.25 \) (not divisible)
- \( 9 \div 5 = 1.8 \) (not divisible)
- \( 9 \div 6 = 1.5 \) (not divisible)
- \( 9 \div 7 = 1.2857 \) (not divisible)
- \( 9 \div 8 = 1.125 \) (not divisible)
- \( 9 \div 9 = 1 \) (remainder 0)

Thus, the factors of 9 are: 1, 3, 9.

#### b) List the factors of 16
To find the factors of 16, we check divisibility from 1 up to 16.

- \( 16 \div 1 = 16 \) (remainder 0)
- \( 16 \div 2 = 8 \) (remainder 0)
- \( 16 \div 3 = 5.3333 \) (not divisible)
- \( 16 \div 4 = 4 \) (remainder 0)
- \( 16 \div 5 = 3.2 \) (not divisible)
- \( 16 \div 6 = 2.6667 \) (not divisible)
- \( 16 \div 7 = 2.2857 \) (not divisible)
- \( 16 \div 8 = 2 \) (remainder 0)
- \( 16 \div 9 = 1.7778 \) (not divisible)
- \( 16 \div 10 = 1.6 \) (not divisible)
- \( 16 \div 11 = 1.4545 \) (not divisible)
- \( 16 \div 12 = 1.3333 \) (not divisible)
- \( 16 \div 13 = 1.2308 \) (not divisible)
- \( 16 \div 14 = 1.1429 \) (not divisible)
- \( 16 \div 15 = 1.0667 \) (not divisible)
- \( 16 \div 16 = 1 \) (remainder 0)

Thus, the factors of 16 are: 1, 2, 4, 8, 16.

#### c) List the factors of 25
To find the factors of 25, we check divisibility from 1 up to 25.

- \( 25 \div 1 = 25 \) (remainder 0)
- \( 25 \div 2 = 12.5 \) (not divisible)
- \( 25 \div 3 = 8.3333 \) (not divisible)
- \( 25 \div 4 = 6.25 \) (not divisible)
- \( 25 \div 5 = 5 \) (remainder 0)
- \( 25 \div 6 = 4.1667 \) (not divisible)
- \( 25 \div 7 = 3.5714 \) (not divisible)
- \( 25 \div 8 = 3.125 \) (not divisible)
- \( 25 \div 9 = 2.7778 \) (not divisible)
- \( 25 \div 10 = 2.5 \) (not divisible)
- \( 25 \div 11 = 2.2727 \) (not divisible)
- \( 25 \div 12 = 2.0833 \) (not divisible)
- \( 25 \div 13 = 1.9231 \) (not divisible)
- \( 25 \div 14 = 1.7857 \) (not divisible)
- \( 25 \div 15 = 1.6667 \) (not divisible)
- \( 25 \div 16 = 1.5625 \) (not divisible)
- \( 25 \div 17 = 1.4706 \) (not divisible)
- \( 25 \div 18 = 1.3889 \) (not divisible)
- \( 25 \div 19 = 1.3158 \) (not divisible)
- \( 25 \div 20 = 1.25 \) (not divisible)
- \( 25 \div 21 = 1.1905 \) (not divisible)
- \( 25 \div 22 = 1.1364 \) (not divisible)
- \( 25 \div 23 = 1.087 \) (not divisible)
- \( 25 \div 24 = 1.0417 \) (not divisible)
- \( 25 \div 25 = 1 \) (remainder 0)

Thus, the factors of 25 are: 1, 5, 25.

#### d) List the factors of 24
To find the factors of 24, we check divisibility from 1 up to 24.

- \( 24 \div 1 = 24 \) (remainder 0)
- \( 24 \div 2 = 12 \) (remainder 0)
- \( 24 \div 3 = 8 \) (remainder 0)
- \( 24 \div 4 = 6 \) (remainder 0)
- \( 24 \div 5 = 4.8 \) (not divisible)
- \( 24 \div 6 = 4 \) (remainder 0)
- \( 24 \div 7 = 3.4286 \) (not divisible)
- \( 24 \div 8 = 3 \) (remainder 0)
- \( 24 \div 9 = 2.6667 \) (not divisible)
- \( 24 \div 10 = 2.4 \) (not divisible)
- \( 24 \div 11 = 2.1818 \) (not divisible)
- \( 24 \div 12 = 2 \) (remainder 0)
- \( 24 \div 13 = 1.8462 \) (not divisible)
- \( 24 \div 14 = 1.7143 \) (not divisible)
- \( 24 \div 15 = 1.6 \) (not divisible)
- \( 24 \div 16 = 1.5 \) (not divisible)
- \( 24 \div 17 = 1.4118 \) (not divisible)
- \( 24 \div 18 = 1.3333 \) (not divisible)
- \( 24 \div 19 = 1.2632 \) (not divisible)
- \( 24 \div 20 = 1.2 \) (not divisible)
- \( 24 \div 21 = 1.1429 \) (not divisible)
- \( 24 \div 22 = 1.0909 \) (not divisible)
- \( 24 \div 23 = 1.0435 \) (not divisible)
- \( 24 \div 24 = 1 \) (remainder 0)

Thus, the factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.

Final Answers:

\[
\boxed{
\text{a) } 1, 3, 9 \\
\text{b) } 1, 2, 4, 8, 16 \\
\text{c) } 1, 5, 25 \\
\text{d) } 1, 2, 3, 4, 6, 8, 12, 24
}
\]