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You’re working on a factors worksheet — the goal is to list all positive factors of each given number. (Note: The worksheet mentions negative factors too, but since the example for 12 only lists positive ones and the blanks are limited, we’ll focus on positive factors, as is standard in elementary math unless otherwise specified.)

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🔢 What is a Factor?

A factor of a number is a whole number that divides it evenly (with no remainder). For example, factors of 12 are 1, 2, 3, 4, 6, 12 because:
- 1 × 12 = 12
- 2 × 6 = 12
- 3 × 4 = 12

We list them in ascending order.

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Let’s solve each one:

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1) 12
Factors: 1, 2, 3, 4, 6, 12

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2) 61
61 is a prime number → only divisible by 1 and itself.
Factors: 1, 61

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3) 69
Check divisibility:
- 69 ÷ 1 = 69
- 69 ÷ 3 = 23 → so 3 and 23 are factors
- 69 ÷ 23 = 3
- 69 ÷ 69 = 1
Factors: 1, 3, 23, 69

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4) 6
Factors: 1, 2, 3, 6

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5) 21
21 ÷ 3 = 7 → so 3 and 7
Factors: 1, 3, 7, 21

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6) 51
51 ÷ 3 = 17 → so 3 and 17
Factors: 1, 3, 17, 51

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7) 22
22 ÷ 2 = 11 → so 2 and 11
Factors: 1, 2, 11, 22

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8) 25
25 = 5 × 5 → perfect square
Factors: 1, 5, 25

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9) 43
43 is prime → only 1 and 43
Factors: 1, 43

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10) 62
62 ÷ 2 = 31 → so 2 and 31
Factors: 1, 2, 31, 62

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11) 61
Same as #2 — prime
Factors: 1, 61

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12) 16
Perfect square: 1×16, 2×8, 4×4
Factors: 1, 2, 4, 8, 16

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13) 98
98 ÷ 2 = 49 → 2 and 49
49 = 7×7 → so also 7 and 14 (since 7×14=98)
Factors: 1, 2, 7, 14, 49, 98

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14) 86
86 ÷ 2 = 43 → so 2 and 43
Factors: 1, 2, 43, 86

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15) 29
29 is prime
Factors: 1, 29

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## ✔ Final Answers (Fill in the blanks):

1) 12 → 1, 2, 3, 4, 6, 12
2) 61 → 1, 61
3) 69 → 1, 3, 23, 69
4) 6 → 1, 2, 3, 6
5) 21 → 1, 3, 7, 21
6) 51 → 1, 3, 17, 51
7) 22 → 1, 2, 11, 22
8) 25 → 1, 5, 25
9) 43 → 1, 43
10) 62 → 1, 2, 31, 62
11) 61 → 1, 61
12) 16 → 1, 2, 4, 8, 16
13) 98 → 1, 2, 7, 14, 49, 98
14) 86 → 1, 2, 43, 86
15) 29 → 1, 29

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💡 Tip: To find factors efficiently:
- Start from 1 and go up.
- For each number `n`, check if it divides the target evenly.
- Stop when you reach the square root — after that, you’ll just repeat factors in reverse.

Let me know if you want to include negative factors too — they’d just be the negatives of all these numbers! 😊