Multiples and factors - Multiplication by URBrainy.com - Free Printable

Problem Analysis:

The worksheet focuses on understanding multiples of numbers and identifying patterns in their units digits. Let's solve each question step by step.

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Question 1: Write down the first ten multiples of 5.

To find the first ten multiples of 5, multiply 5 by the numbers 1 through 10:
\[
5 \times 1 = 5, \quad 5 \times 2 = 10, \quad 5 \times 3 = 15, \quad 5 \times 4 = 20, \quad 5 \times 5 = 25,
\]
\[
5 \times 6 = 30, \quad 5 \times 7 = 35, \quad 5 \times 8 = 40, \quad 5 \times 9 = 45, \quad 5 \times 10 = 50.
\]

Answer:
\[
5, 10, 15, 20, 25, 30, 35, 40, 45, 50
\]

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Question 2: What do you notice? Look especially at the units digits.

The units digits of the multiples of 5 are:
\[
5, 0, 5, 0, 5, 0, 5, 0, 5, 0
\]
We observe that the units digit alternates between 5 and 0.

Answer:
The units digits alternate between 5 and 0.

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Question 3: Which of these numbers are multiples of 5? Circle them.

Given numbers: \( 26, 60, 10, 44, 35, 95, 111 \)

A number is a multiple of 5 if its units digit is either 0 or 5. Checking each number:
- \( 26 \): Units digit is 6 (not a multiple of 5)
- \( 60 \): Units digit is 0 (multiple of 5)
- \( 10 \): Units digit is 0 (multiple of 5)
- \( 44 \): Units digit is 4 (not a multiple of 5)
- \( 35 \): Units digit is 5 (multiple of 5)
- \( 95 \): Units digit is 5 (multiple of 5)
- \( 111 \): Units digit is 1 (not a multiple of 5)

Answer:
Circle \( 60, 10, 35, 95 \).

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Question 4: Write down the first ten multiples of 10.

To find the first ten multiples of 10, multiply 10 by the numbers 1 through 10:
\[
10 \times 1 = 10, \quad 10 \times 2 = 20, \quad 10 \times 3 = 30, \quad 10 \times 4 = 40, \quad 10 \times 5 = 50,
\]
\[
10 \times 6 = 60, \quad 10 \times 7 = 70, \quad 10 \times 8 = 80, \quad 10 \times 9 = 90, \quad 10 \times 10 = 100.
\]

Answer:
\[
10, 20, 30, 40, 50, 60, 70, 80, 90, 100
\]

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Question 5: What do you notice? Look especially at the units digit.

The units digits of the multiples of 10 are:
\[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
\]
We observe that the units digit is always 0.

Answer:
The units digit is always 0.

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Question 6: Which of these numbers are multiples of 10? Circle them.

Given numbers: \( 49, 30, 212, 120, 50, 99, 200 \)

A number is a multiple of 10 if its units digit is 0. Checking each number:
- \( 49 \): Units digit is 9 (not a multiple of 10)
- \( 30 \): Units digit is 0 (multiple of 10)
- \( 212 \): Units digit is 2 (not a multiple of 10)
- \( 120 \): Units digit is 0 (multiple of 10)
- \( 50 \): Units digit is 0 (multiple of 10)
- \( 99 \): Units digit is 9 (not a multiple of 10)
- \( 200 \): Units digit is 0 (multiple of 10)

Answer:
Circle \( 30, 120, 50, 200 \).

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Question 7: Write down the first ten multiples of 2.

To find the first ten multiples of 2, multiply 2 by the numbers 1 through 10:
\[
2 \times 1 = 2, \quad 2 \times 2 = 4, \quad 2 \times 3 = 6, \quad 2 \times 4 = 8, \quad 2 \times 5 = 10,
\]
\[
2 \times 6 = 12, \quad 2 \times 7 = 14, \quad 2 \times 8 = 16, \quad 2 \times 9 = 18, \quad 2 \times 10 = 20.
\]

Answer:
\[
2, 4, 6, 8, 10, 12, 14, 16, 18, 20
\]

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Question 8: What do you notice? Again look especially at the units digits.

The units digits of the multiples of 2 are:
\[
2, 4, 6, 8, 0, 2, 4, 6, 8, 0
\]
We observe that the units digits repeat in a cycle: 2, 4, 6, 8, 0.

Answer:
The units digits repeat in the cycle 2, 4, 6, 8, 0.

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Question 9: Which of these numbers are multiples of 2? Circle them.

Given numbers: \( 34, 45, 56, 67, 78, 89, 90 \)

A number is a multiple of 2 if it is even (i.e., its units digit is 0, 2, 4, 6, or 8). Checking each number:
- \( 34 \): Units digit is 4 (even, multiple of 2)
- \( 45 \): Units digit is 5 (odd, not a multiple of 2)
- \( 56 \): Units digit is 6 (even, multiple of 2)
- \( 67 \): Units digit is 7 (odd, not a multiple of 2)
- \( 78 \): Units digit is 8 (even, multiple of 2)
- \( 89 \): Units digit is 9 (odd, not a multiple of 2)
- \( 90 \): Units digit is 0 (even, multiple of 2)

Answer:
Circle \( 34, 56, 78, 90 \).

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Question 10: Which of these numbers are multiples of both 2 and 5? Circle them.

Given numbers: \( 44, 50, 24, 30, 26, 10, 11 \)

A number is a multiple of both 2 and 5 if it is a multiple of their least common multiple (LCM). The LCM of 2 and 5 is 10. Therefore, the number must be a multiple of 10. Checking each number:
- \( 44 \): Not a multiple of 10
- \( 50 \): Multiple of 10
- \( 24 \): Not a multiple of 10
- \( 30 \): Multiple of 10
- \( 26 \): Not a multiple of 10
- \( 10 \): Multiple of 10
- \( 11 \): Not a multiple of 10

Answer:
Circle \( 50, 30, 10 \).

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Final Answers:

1. \( 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 \)
2. The units digits alternate between 5 and 0.
3. Circle \( 60, 10, 35, 95 \)
4. \( 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 \)
5. The units digit is always 0.
6. Circle \( 30, 120, 50, 200 \)
7. \( 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 \)
8. The units digits repeat in the cycle 2, 4, 6, 8, 0.
9. Circle \( 34, 56, 78, 90 \)
10. Circle \( 50, 30, 10 \)

\boxed{5, 10, 15, 20, 25, 30, 35, 40, 45, 50}
\boxed{60, 10, 35, 95}
\boxed{10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
\boxed{30, 120, 50, 200}
\boxed{2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
\boxed{34, 56, 78, 90}
\boxed{50, 30, 10}