Math worksheet on understanding and using factors with multiple-choice questions.

Let's solve each question step by step from the worksheet titled "Understanding and Using Factors".

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1. Which number is a factor of 57?

Options:
① 11 ② 13 ③ 17 ④ 19

Step-by-step:
We need to find which of these numbers divides 57 evenly (no remainder).

- 57 ÷ 11 = 5.18... → Not a whole number ✘
- 57 ÷ 13 ≈ 4.38 → Not a whole number ✘
- 57 ÷ 17 ≈ 3.35 → Not a whole number ✘
- 57 ÷ 19 = 3 → Exactly! ✔

So, 19 × 3 = 57, so 19 is a factor.

✔ Answer: ④ 19

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2. What are all the factors of 8?

Options:
① 1,8 ② 2,4 ③ 1,4,8 ④ 1,2,4,8

Step-by-step:
List all numbers that divide 8 evenly:

- 1 × 8 = 8
- 2 × 4 = 8
- 4 × 2 = 8 (already listed)
- 8 × 1 = 8 (already listed)

So the factors are: 1, 2, 4, 8

✔ Answer: ④ 1, 2, 4, 8

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3. What are the common factors of 8, 24, and 60?

Options:
① 1, 2, 4 ② 1, 2, 4, 6 ③ 1, 2, 4, 6, 8

Step-by-step:
Find factors of each number:

- Factors of 8: 1, 2, 4, 8
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Now, find common ones in all three:

- Common: 1, 2, 4

(6 is not a factor of 8 → so not common)

✔ Answer: ① 1, 2, 4

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4. A play sold $90 worth of tickets. Each ticket cost the same amount. Which of these could be the cost of each ticket?

Options:
① $16 ② $50 ③ $18 ④ $24

We need to find which of these amounts divides evenly into $90.

Check each:

- 90 ÷ 16 = 5.625 → Not a whole number ✘
- 90 ÷ 50 = 1.8 → Not a whole number ✘
- 90 ÷ 18 = 5 → Yes! ✔
- 90 ÷ 24 = 3.75 → No ✘

So only $18 divides evenly into $90.

✔ Answer: ③ $18

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5. What factors do 12, 24, and 36 have in common? Select all that apply.

Options:
□ 3 □ 9 □ 12 □ 18

Find common factors of 12, 24, and 36.

First, list factors:

- 12: 1, 2, 3, 4, 6, 12
- 24: 1, 2, 3, 4, 6, 8, 12, 24
- 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Common factors: 1, 2, 3, 4, 6, 12

Now check options:

- 3 → ✔ Yes
- 9 → ✘ (not a factor of 12 or 24)
- 12 → ✔ Yes
- 18 → ✘ (not a factor of 12 or 24)

✔ Answers: 3 and 12

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6. Jennifer divided 76 coins into equal piles. Which of these could be the number of coins in each pile? Select all that apply.

Options:
□ 2 □ 3 □ 4 □ 5 □ 6 □ 7 □ 8 □ 9 □ 11 □ 13 □ 17 □ 19

We need to find which of these numbers divide 76 evenly.

Check each:

- 76 ÷ 2 = 38 → ✔
- 76 ÷ 3 ≈ 25.33 → ✘
- 76 ÷ 4 = 19 → ✔
- 76 ÷ 5 = 15.2 → ✘
- 76 ÷ 6 ≈ 12.67 → ✘
- 76 ÷ 7 ≈ 10.86 → ✘
- 76 ÷ 8 = 9.5 → ✘
- 76 ÷ 9 ≈ 8.44 → ✘
- 76 ÷ 11 ≈ 6.91 → ✘
- 76 ÷ 13 ≈ 5.85 → ✘
- 76 ÷ 17 ≈ 4.47 → ✘
- 76 ÷ 19 = 4 → ✔

So valid divisors: 2, 4, 19

✔ Answers: 2, 4, 19

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✔ Final Answers Summary:

1. ④ 19
2. ④ 1, 2, 4, 8
3. ① 1, 2, 4
4. ③ $18
5. 3, 12
6. 2, 4, 19

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