Let's solve each part of the worksheet step by step.
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Understanding Factors
Factors are numbers that divide exactly into another number (with no remainder). For example:
- The factors of 12: 1, 2, 3, 4, 6, 12 — because all these divide 12 evenly.
- They can be paired as:
$1 \times 12 = 12$,
$2 \times 6 = 12$,
$3 \times 4 = 12$
We'll use this method to find the factors for each number.
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a) List the factors of 9
We look for all whole numbers that divide 9 exactly.
Start from 1 and check:
- $1 \times 9 = 9$ → both 1 and 9 are factors
- $3 \times 3 = 9$ → 3 is a factor
- Try 2: $9 ÷ 2 = 4.5$ → not a whole number → not a factor
- Try 4: $9 ÷ 4 = 2.25$ → no
- 5, 6, 7, 8: none divide 9 evenly
So the factors of 9 are:
1, 3, 9
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✔ Answer:
1, 3, 9
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b) List the factors of 16
Check which numbers divide 16 exactly:
- $1 \times 16 = 16$
- $2 \times 8 = 16$
- $4 \times 4 = 16$
- $3$: $16 ÷ 3 ≈ 5.33$ → no
- $5$: $16 ÷ 5 = 3.2$ → no
- $6, 7, 9, 10, ...$ → too big or don’t divide evenly
So the factors are:
1, 2, 4, 8, 16
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✔ Answer:
1, 2, 4, 8, 16
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c) List the factors of 25
Check divisors:
- $1 \times 25 = 25$
- $5 \times 5 = 25$
- $2$: $25 ÷ 2 = 12.5$ → no
- $3$: $25 ÷ 3 ≈ 8.33$ → no
- $4$: $25 ÷ 4 = 6.25$ → no
- $6, 7, ..., 24$: none divide 25 evenly
So the factors are:
1, 5, 25
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✔ Answer:
1, 5, 25
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d) List the factors of 24
Find all numbers that divide 24 evenly:
- $1 \times 24 = 24$
- $2 \times 12 = 24$
- $3 \times 8 = 24$
- $4 \times 6 = 24$
- $5$: $24 ÷ 5 = 4.8$ → no
- $7$: $24 ÷ 7 ≈ 3.43$ → no
- $9, 10, 11, 13, ...$: too big or not divisible
So the factors are:
1, 2, 3, 4, 6, 8, 12, 24
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✔ Answer:
1, 2, 3, 4, 6, 8, 12, 24
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✔ Final Answers:
a) Factors of 9:
1, 3, 9
b) Factors of 16:
1, 2, 4, 8, 16
c) Factors of 25:
1, 5, 25
d) Factors of 24:
1, 2, 3, 4, 6, 8, 12, 24
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💡
Tip: To find factors efficiently, test numbers from 1 up to the square root of the number. Once you find a pair, list both numbers. This avoids repetition and saves time.
Parent Tip: Review the logic above to help your child master the concept of math worksheet for factors and multiples.
