Factor Rainbow Worksheets - Math Monks - Free Printable

You're working on a Factor Rainbows worksheet — a fun, visual way to find all the factor pairs of a number.

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✔ What is a Factor Pair?

A factor pair is two numbers that multiply together to give the target number.
Example: For 20 → (1, 20), (2, 10), (4, 5) are factor pairs because:
- 1 × 20 = 20
- 2 × 10 = 20
- 4 × 5 = 20

In a factor rainbow, you write the smallest factor on the left and its pair on the right, then move inward until you meet in the middle.

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Let’s solve each one:

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1) Number: 20

Already filled for you as an example.
✔ Factor pairs: (1,20), (2,10), (4,5)

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2) Number: 15

Find all factor pairs:
- 1 × 15 = 15 → (1, 15)
- 3 × 5 = 15 → (3, 5)

No more whole number pairs.

🟩 Answer:
Left to right: 1, 3, 5, 15

*(Rainbow arcs: 1–15, 3–5)*

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3) Number: 8

Factor pairs:
- 1 × 8 = 8 → (1, 8)
- 2 × 4 = 8 → (2, 4)

🟩 Answer:
Left to right: 1, 2, 4, 8

*(Rainbow arcs: 1–8, 2–4)*

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4) Number: 24

Factor pairs:
- 1 × 24 = 24 → (1, 24)
- 2 × 12 = 24 → (2, 12)
- 3 × 8 = 24 → (3, 8)
- 4 × 6 = 24 → (4, 6)

🟩 Answer:
Left to right: 1, 2, 3, 4, 6, 8, 12, 24

*(Rainbow arcs: 1–24, 2–12, 3–8, 4–6)*

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5) Number: 10

Factor pairs:
- 1 × 10 = 10 → (1, 10)
- 2 × 5 = 10 → (2, 5)

🟩 Answer:
Left to right: 1, 2, 5, 10

*(Rainbow arcs: 1–10, 2–5)*

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6) Number: 18

Factor pairs:
- 1 × 18 = 18 → (1, 18)
- 2 × 9 = 18 → (2, 9)
- 3 × 6 = 18 → (3, 6)

🟩 Answer:
Left to right: 1, 2, 3, 6, 9, 18

*(Rainbow arcs: 1–18, 2–9, 3–6)*

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7) Number: 36

Factor pairs:
- 1 × 36 = 36 → (1, 36)
- 2 × 18 = 36 → (2, 18)
- 3 × 12 = 36 → (3, 12)
- 4 × 9 = 36 → (4, 9)
- 6 × 6 = 36 → (6, 6) ← middle!

🟩 Answer:
Left to right: 1, 2, 3, 4, 6, 9, 12, 18, 36

*(Rainbow arcs: 1–36, 2–18, 3–12, 4–9, 6–6 [center])*

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8) Number: 30

Factor pairs:
- 1 × 30 = 30 → (1, 30)
- 2 × 15 = 30 → (2, 15)
- 3 × 10 = 30 → (3, 10)
- 5 × 6 = 30 → (5, 6)

🟩 Answer:
Left to right: 1, 2, 3, 5, 6, 10, 15, 30

*(Rainbow arcs: 1–30, 2–15, 3–10, 5–6)*

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9) Number: 12

Factor pairs:
- 1 × 12 = 12 → (1, 12)
- 2 × 6 = 12 → (2, 6)
- 3 × 4 = 12 → (3, 4)

🟩 Answer:
Left to right: 1, 2, 3, 4, 6, 12

*(Rainbow arcs: 1–12, 2–6, 3–4)*

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## 🎯 Final Answers Summary:

| Problem | Factors (Left to Right) |
|---------|---------------------------------------------|
| 1 | 1, 2, 4, 5, 10, 20 |
| 2 | 1, 3, 5, 15 |
| 3 | 1, 2, 4, 8 |
| 4 | 1, 2, 3, 4, 6, 8, 12, 24 |
| 5 | 1, 2, 5, 10 |
| 6 | 1, 2, 3, 6, 9, 18 |
| 7 | 1, 2, 3, 4, 6, 9, 12, 18, 36 |
| 8 | 1, 2, 3, 5, 6, 10, 15, 30 |
| 9 | 1, 2, 3, 4, 6, 12 |

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💡 Tip: Always start with 1 and the number itself, then check 2, 3, 4… up to the square root of the number. Once you pass the square root, you’ll just repeat pairs in reverse.

Let me know if you want to draw the rainbows or need help understanding why we stop at the square root! 🌈