Multiples and Factors worksheet for practicing identifying multiples of numbers 2, 3, 5, and 10.

Absolutely! Let’s solve each question step by step and explain the reasoning behind each answer.

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1. Write down the first ten multiples of 5.

Multiples of 5 are found by multiplying 5 by whole numbers: 1, 2, 3, ..., 10.

Answer:
> 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

✔ *Explanation:*
5 × 1 = 5
5 × 2 = 10
5 × 3 = 15
...
5 × 10 = 50

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

Look at the last digit (units digit) of each multiple from Question 1:

5, 10, 15, 20, 25, 30, 35, 40, 45, 50 → Units digits: 5, 0, 5, 0, 5, 0, 5, 0, 5, 0

Answer:
> The units digit alternates between 5 and 0. All multiples of 5 end in either 0 or 5.

✔ *Explanation:*
This is a key divisibility rule — any number ending in 0 or 5 is divisible by 5.

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

Numbers: 26, 60, 10, 44, 35, 95, 111

Check which numbers end in 0 or 5:

- 26 → ends in 6 → ✘
- 60 → ends in 0 → ✔
- 10 → ends in 0 → ✔
- 44 → ends in 4 → ✘
- 35 → ends in 5 → ✔
- 95 → ends in 5 → ✔
- 111 → ends in 1 → ✘

Answer:
> Circle: 60, 10, 35, 95

✔ *Explanation:* Again, using the rule — if it ends in 0 or 5, it’s a multiple of 5.

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4. Write down the first ten multiples of 10.

Multiply 10 by 1 through 10.

Answer:
> 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

✔ *Explanation:*
10 × 1 = 10
10 × 2 = 20
...
10 × 10 = 100

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

Look at the units digits:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100 → all end in 0

Answer:
> All multiples of 10 end in 0.

✔ *Explanation:* This is the divisibility rule for 10 — a number must end in 0 to be divisible by 10.

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

Numbers: 49, 30, 212, 120, 50, 99, 200

Check which end in 0:

- 49 → ends in 9 → ✘
- 30 → ends in 0 → ✔
- 212 → ends in 2 → ✘
- 120 → ends in 0 → ✔
- 50 → ends in 0 → ✔
- 99 → ends in 9 → ✘
- 200 → ends in 0 → ✔

Answer:
> Circle: 30, 120, 50, 200

✔ *Explanation:* Only numbers ending in 0 are multiples of 10.

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7. Write down the first ten multiples of 2.

Multiply 2 by 1 through 10.

Answer:
> 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

✔ *Explanation:*
2 × 1 = 2
2 × 2 = 4
...
2 × 10 = 20

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

Units digits: 2, 4, 6, 8, 0, 2, 4, 6, 8, 0 → all even digits!

Answer:
> All multiples of 2 end in an even digit: 0, 2, 4, 6, or 8. These are called even numbers.

✔ *Explanation:* The divisibility rule for 2 — if the last digit is even, the number is divisible by 2.

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

Numbers: 34, 45, 56, 67, 78, 89, 90

Check for even units digit:

- 34 → ends in 4 → ✔
- 45 → ends in 5 → ✘
- 56 → ends in 6 → ✔
- 67 → ends in 7 → ✘
- 78 → ends in 8 → ✔
- 89 → ends in 9 → ✘
- 90 → ends in 0 → ✔

Answer:
> Circle: 34, 56, 78, 90

✔ *Explanation:* Even numbers (ending in 0,2,4,6,8) are multiples of 2.

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

Numbers: 44, 50, 24, 30, 26, 10, 11

To be a multiple of both 2 and 5, a number must satisfy:
- End in 0 (because only 0 satisfies both rules: even AND divisible by 5)

Check:

- 44 → ends in 4 → ✘
- 50 → ends in 0 → ✔
- 24 → ends in 4 → ✘
- 30 → ends in 0 → ✔
- 26 → ends in 6 → ✘
- 10 → ends in 0 → ✔
- 11 → ends in 1 → ✘

Answer:
> Circle: 50, 30, 10

✔ *Explanation:* A number divisible by both 2 and 5 must be divisible by 10 (since 2×5=10), so it must end in 0.

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## ✔ Final Summary of Answers:

1. 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
2. They all end in 0 or 5.
3. Circle: 60, 10, 35, 95
4. 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
5. They all end in 0.
6. Circle: 30, 120, 50, 200
7. 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
8. They all end in even digits (0,2,4,6,8).
9. Circle: 34, 56, 78, 90
10. Circle: 50, 30, 10

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Let me know if you’d like this formatted as a printable worksheet or want to learn more about factors too! 😊