Factor Rainbow Worksheet | PDF - Free Printable

To solve this "Factor Rainbows" task, we need to find all the factor pairs for each number shown in the cloud. A factor pair is two numbers that multiply together to give you the target number.

Let’s go step by step for each problem:

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Problem 1: Number = 20

We already have some factors filled in: 1, 2, 4, 5, 10, 20 — these are correct!
Pairs:
1 × 20 = 20 → outermost rainbow
2 × 10 = 20 → middle rainbow
4 × 5 = 20 → innermost rainbow
✔ Already complete.

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Problem 2: Number = 15

Find all factor pairs of 15:
1 × 15 = 15
3 × 5 = 15
So the four boxes should be: 1, 3, 5, 15

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Problem 3: Number = 8

Factor pairs of 8:
1 × 8 = 8
2 × 4 = 8
So the four boxes should be: 1, 2, 4, 8

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Problem 4: Number = 24

Factor pairs of 24:
1 × 24 = 24
2 × 12 = 24
3 × 8 = 24
4 × 6 = 24
So the eight boxes should be: 1, 2, 3, 4, 6, 8, 12, 24

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Problem 5: Number = 10

Factor pairs of 10:
1 × 10 = 10
2 × 5 = 10
So the four boxes should be: 1, 2, 5, 10

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Problem 6: Number = 18

Factor pairs of 18:
1 × 18 = 18
2 × 9 = 18
3 × 6 = 18
So the six boxes should be: 1, 2, 3, 6, 9, 18

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Problem 7: Number = 36

Factor pairs of 36:
1 × 36 = 36
2 × 18 = 36
3 × 12 = 36
4 × 9 = 36
6 × 6 = 36 ← but since it’s a pair, we write 6 once? Wait — no! In factor rainbows, even if a number is a perfect square, we still list both factors — but since 6×6 is the same number, we only write 6 once in the middle? Actually, looking at the answer key style from earlier problems, they list all factors in order without repeating. Let’s check:

Actually, in problem 4 (24), they listed 1,2,3,4,6,8,12,24 — that’s 8 factors. For 36, factors are: 1, 2, 3, 4, 6, 9, 12, 18, 36 — that’s 9 factors. But the rainbow has 8 boxes? Wait — let me count the boxes in problem 7.

Looking back at the image description: Problem 7 has 8 boxes total — 4 on left, 4 on right? Or maybe 4 on each side? Actually, in the original problem statement, for problem 7, it shows 8 empty boxes under the rainbow. But 36 has 9 factors. Hmm.

Wait — perhaps I miscounted. Let me think differently.

In factor rainbows, you list factors in ascending order, and connect them in pairs from outside in. For 36:

Factors: 1, 2, 3, 4, 6, 9, 12, 18, 36 → that’s 9 numbers. But the rainbow diagram for problem 7 likely has 8 boxes? That doesn’t match.

Wait — looking at the “Answers” section provided in the image description, for problem 7, it’s cut off, but for problem 4 (24), they had 8 boxes and listed 8 factors. For 36, which has 9 factors, maybe the diagram expects us to list all 9? But the box count might be wrong.

Actually, let’s look at problem 8: 30. Factors of 30: 1,2,3,5,6,10,15,30 → 8 factors. So probably each rainbow has space for all factors.

But for 36, there are 9 factors. Perhaps the diagram allows for 9 boxes? Or maybe I made a mistake.

Wait — let’s list factors of 36 properly:

1, 2, 3, 4, 6, 9, 12, 18, 36 → yes, 9 factors.

But in the answer key example for problem 4 (24), they listed 8 factors in 8 boxes. So for 36, we need 9 boxes? The diagram might have 9 boxes — perhaps I miscounted.

Since the user didn’t provide the full answer key for problems 7-9, I’ll proceed with correct math.

For problem 7: 36 → factors: 1, 2, 3, 4, 6, 9, 12, 18, 36

But the rainbow connects pairs: 1-36, 2-18, 3-12, 4-9, and 6-6. Since 6 is repeated, in some diagrams they write it once in the center. But in the given examples, like problem 4 (24), they didn’t have a perfect square, so no issue.

Looking at problem 9: 12 — factors: 1,2,3,4,6,12 → 6 factors. Diagram likely has 6 boxes.

I think for consistency, we list all factors in ascending order in the boxes.

So for problem 7: 36 → boxes: 1, 2, 3, 4, 6, 9, 12, 18, 36

But if the diagram has only 8 boxes, that’s a problem. However, since the answer key for problem 4 had 8 boxes for 8 factors, and 36 has 9, perhaps the diagram for problem 7 has 9 boxes. I’ll assume that.

Similarly, problem 8: 30 → factors: 1,2,3,5,6,10,15,30 → 8 factors.

Problem 9: 12 → factors: 1,2,3,4,6,12 → 6 factors.

Now, let’s finalize:

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Final Answers for Each Problem:

1) 20 — already done: 1, 2, 4, 5, 10, 20

2) 15 → 1, 3, 5, 15

3) 8 → 1, 2, 4, 8

4) 24 → 1, 2, 3, 4, 6, 8, 12, 24

5) 10 → 1, 2, 5, 10

6) 18 → 1, 2, 3, 6, 9, 18

7) 36 → 1, 2, 3, 4, 6, 9, 12, 18, 36

8) 30 → 1, 2, 3, 5, 6, 10, 15, 30

9) 12 → 1, 2, 3, 4, 6, 12

Note: For problem 7, if the diagram has only 8 boxes, it might be an error, but mathematically, 36 has 9 factors. Since the answer key for problem 4 had 8 boxes for 8 factors, and 36 has 9, I suspect the diagram for problem 7 has 9 boxes. If not, perhaps they expect to omit one, but that would be incorrect. I’ll go with the correct mathematical answer.

Similarly, for problem 9, 12 has 6 factors, so 6 boxes.

Now, to present the final answer as requested — since the user wants the solution, and the task is to fill in the blanks, I’ll list the numbers for each problem in order.

But the instruction says: "Provide only the final correct answer — this should come AFTER all explanations and reasoning."

And since the user didn't specify which problem to solve, but the image has multiple, I think I need to provide all.

However, the response format says "Final Answer" should be the final correct answer — perhaps for all problems.

Given that, I'll list them as:

Final Answer:
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

But to match the rainbow format, perhaps list them in the order they appear in the boxes — left to right, ascending order.

Yes, that's what I have.

I think this is correct.