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

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

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1. Write down the first ten multiples of 5.

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

🔹 Explanation:
Multiples of 5 are found by multiplying 5 by whole numbers 1 through 10:
- 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.

✔ Answer:
All multiples of 5 end in either 0 or 5.

🔹 Explanation:
Looking at the units digit (the last digit) of the multiples from Question 1:
- 5 → ends in 5
- 10 → ends in 0
- 15 → ends in 5
- 20 → ends in 0
- ... and so on.

This pattern continues forever — every multiple of 5 will always end in 0 or 5.

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

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

✔ Answer (Circle these):
60, 10, 35, 95

🔹 Explanation:
Use the rule from Q2: if a number ends in 0 or 5, it’s a multiple of 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 → ✘

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4. Write down the first ten multiples of 10.

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

🔹 Explanation:
Multiply 10 by whole numbers 1 to 10:
- 10 × 1 = 10
- 10 × 2 = 20
- ...
- 10 × 10 = 100

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

✔ Answer:
All multiples of 10 end in 0.

🔹 Explanation:
From the list above: 10, 20, 30, ..., 100 — every number ends with a zero. This is because multiplying any whole number by 10 adds a zero at the end.

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

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

✔ Answer (Circle these):
30, 120, 50, 200

🔹 Explanation:
Apply the rule: multiples of 10 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 → ✔

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7. Write down the first ten multiples of 2.

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

🔹 Explanation:
Multiply 2 by whole numbers 1 through 10:
- 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.

✔ Answer:
All multiples of 2 end in 0, 2, 4, 6, or 8 — i.e., they are even numbers.

🔹 Explanation:
The units digits in the multiples of 2 are:
- 2, 4, 6, 8, 0, 2, 4, 6, 8, 0 → repeating pattern.

Any number ending in an even digit is divisible by 2 — that’s the definition of an even number!

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

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

✔ Answer (Circle these):
34, 56, 78, 90

🔹 Explanation:
Check the units digit — if it’s even (0,2,4,6,8), it’s a multiple of 2.
- 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 → ✔

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

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

✔ Answer (Circle these):
50, 30, 10

🔹 Explanation:
A number that is a multiple of both 2 and 5 must be a multiple of 10 (since 2 × 5 = 10).

So, apply the rule from Q5: multiples of 10 end in 0.

Check each number:
- 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 → ✘

✔ So only 50, 30, and 10 are multiples of both 2 and 5.

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## 🎯 Summary of Key Rules:

| Number | Rule for Multiples |
|--------|--------------------|
| 2 | Ends in 0, 2, 4, 6, or 8 (even numbers) |
| 5 | Ends in 0 or 5 |
| 10 | Ends in 0 |
| 2 AND 5 | Must end in 0 (i.e., multiple of 10) |

These patterns help quickly identify multiples without doing full division!

Let me know if you’d like to print this as a completed worksheet or need more practice 😊