Let’s work through each factor rainbow step by step.
A “factor rainbow” is a way to show all the factor pairs of a number. You start with 1 and the number itself, then find the next pair (like 2 and whatever multiplies with 2 to get the number), and keep going until you reach the middle. Each pair connects with an arc — like a rainbow.
We’ll go one by one.
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Problem 1: Number = 15
Factors of 15:
- 1 × 15 → write 1 and 15
- 3 × 5 → write 3 and 5
- Next would be 5 × 3 — but we already have that, so stop.
So factors in order: 1, 3, 5, 15
Rainbow arcs:
- Outer arc: 1 — 15
- Inner arc: 3 — 5
✔ Done.
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Problem 2: Number = 20
Factors:
- 1 × 20
- 2 × 10
- 4 × 5
- Next is 5 × 4 — already done.
Factors in order: 1, 2, 4, 5, 10, 20
Rainbow arcs:
- 1 — 20
- 2 — 10
- 4 — 5
✔ Done.
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Problem 3: Number = 16
Factors:
- 1 × 16
- 2 × 8
- 4 × 4 → this is the middle, so we write 4 once in the center.
Factors in order: 1, 2, 4, 8, 16
Rainbow arcs:
- 1 — 16
- 2 — 8
- 4 (center)
✔ Done.
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Problem 4: Number = 70
Factors:
- 1 × 70
- 2 × 35
- 5 × 14
- 7 × 10
- Next is 10 × 7 — already done.
Factors in order: 1, 2, 5, 7, 10, 14, 35, 70
Rainbow arcs:
- 1 — 70
- 2 — 35
- 5 — 14
- 7 — 10
✔ Done.
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Problem 5: Number = 32
Factors:
- 1 × 32
- 2 × 16
- 4 × 8
- Next is 8 × 4 — already done.
Factors in order: 1, 2, 4, 8, 16, 32
Rainbow arcs:
- 1 — 32
- 2 — 16
- 4 — 8
✔ Done.
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Problem 6: Number = 50
Factors:
- 1 × 50
- 2 × 25
- 5 × 10
- Next is 10 × 5 — already done.
Factors in order: 1, 2, 5, 10, 25, 50
Rainbow arcs:
- 1 — 50
- 2 — 25
- 5 — 10
✔ Done.
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Problem 7: Number = 18
Factors:
- 1 × 18
- 2 × 9
- 3 × 6
- Next is 6 × 3 — already done.
Factors in order: 1, 2, 3, 6, 9, 18
Rainbow arcs:
- 1 — 18
- 2 — 9
- 3 — 6
✔ Done.
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Problem 8: Number = 21
Factors:
- 1 × 21
- 3 × 7
- Next is 7 × 3 — already done.
Factors in order: 1, 3, 7, 21
Rainbow arcs:
- 1 — 21
- 3 — 7
✔ Done.
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Problem 9: Number = 12
Factors:
- 1 × 12
- 2 × 6
- 3 × 4
- Next is 4 × 3 — already done.
Factors in order: 1, 2, 3, 4, 6, 12
Rainbow arcs:
- 1 — 12
- 2 — 6
- 3 — 4
✔ Done.
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Problems 10–12: Create your own factor rainbows
You need to draw the rainbow and label each factor.
Problem 10: Number = 7
7 is prime → only factors are 1 and 7.
Factor rainbow:
- One arc: 1 — 7
Problem 11: Number = 9
Factors:
- 1 × 9
- 3 × 3 → middle
Factors: 1, 3, 9
Rainbow:
- 1 — 9
- 3 (center)
Problem 12: Number = 24
Factors:
- 1 × 24
- 2 × 12
- 3 × 8
- 4 × 6
- Next is 6 × 4 — already done.
Factors: 1, 2, 3, 4, 6, 8, 12, 24
Rainbow arcs:
- 1 — 24
- 2 — 12
- 3 — 8
- 4 — 6
✔ All done!
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Final Answer:
1. Factors of 15: 1, 3, 5, 15
2. Factors of 20: 1, 2, 4, 5, 10, 20
3. Factors of 16: 1, 2, 4, 8, 16
4. Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
5. Factors of 32: 1, 2, 4, 8, 16, 32
6. Factors of 50: 1, 2, 5, 10, 25, 50
7. Factors of 18: 1, 2, 3, 6, 9, 18
8. Factors of 21: 1, 3, 7, 21
9. Factors of 12: 1, 2, 3, 4, 6, 12
10. Factors of 7: 1, 7
11. Factors of 9: 1, 3, 9
12. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Parent Tip: Review the logic above to help your child master the concept of rainbow factors worksheet.
