Students solve GCF problems to navigate a math maze.

Let's solve the Greatest Common Factor (GCF) maze step by step based on the image you provided.

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🔹 Understanding the Task

We are given a maze where each box contains two numbers. We must find the GCF of each pair and use that number to determine which path to follow (the GCF will match one of the numbers on the arrows between boxes).

We start at the "Start" box with the pair:
👉 15, 40

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✔ Step 1: Find GCF of 15 and 40

We can use prime factorization or division method.

#### Prime Factorization:
- 15 = 3 × 5
- 40 = 2³ × 5

Common factor: 5

✔ So, GCF(15, 40) = 5

From the "Start" box, there is an arrow labeled 5 going to the next box: 12, 54

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✔ Step 2: Find GCF of 12 and 54

- 12 = 2² × 3
- 54 = 2 × 3³

Common factors: 2 × 3 = 6

✔ GCF(12, 54) = 6

Now look for the arrow labeled 6 from this box → leads to 39, 26

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✔ Step 3: Find GCF of 39 and 26

- 39 = 3 × 13
- 26 = 2 × 13

Common factor: 13

✔ GCF(39, 26) = 13

Arrow labeled 13 leads to 24, 64

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✔ Step 4: Find GCF of 24 and 64

- 24 = 2³ × 3
- 64 = 2⁶

Common factor: 2³ = 8

✔ GCF(24, 64) = 8

Arrow labeled 8 leads to ... (next box)

Wait — in your image, we see:

From 39, 26, the 13 goes to 24, 64, and then from 24, 64, there’s an arrow labeled 8 leading down.

But what comes after? Let's check other paths.

Also, from earlier:

- From 15, 40 → GCF = 5 → go to 12, 54
- Then 12, 54 → GCF = 6 → go to 39, 26
- Then 39, 26 → GCF = 13 → go to 24, 64
- Then 24, 64 → GCF = 8 → now we need to see where 8 leads

Looking at the diagram:

From 24, 64, the arrow labeled 8 goes down to another box.

But we also have 35, 28 above.

Let’s check 35, 28 as well.

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✔ Step 5: Check 35, 28

- 35 = 5 × 7
- 28 = 2² × 7

Common factor: 7

✔ GCF(35, 28) = 7

So if we had gone from 12, 54 → 35, 28 via arrow 9, but GCF was 6, so we don’t take that path.

But wait — from 12, 54, we have two exits:

- Arrow 6 → to 39, 26
- Arrow 9 → to 35, 28

But since GCF(12,54) = 6, we must go via 6, not 9.

So we skip 35,28 unless we get there through another route.

Now back to our path:

We are at 24, 64, GCF = 8 → arrow 8 goes down.

Let’s assume the path continues.

But let’s look at 50, 40 — it’s connected to 15,40 via arrow 7

But GCF(15,40) = 5 → so we don’t go to 50,40 via 7.

So only valid path is:

> Start (15,40) → GCF = 5 → → 12,54
> 12,54 → GCF = 6 → → 39,26
> 39,26 → GCF = 13 → → 24,64
> 24,64 → GCF = 8 → → ??

Now, from 24,64, arrow 8 leads to a box below.

Let’s suppose the next box is something, and the arrow is labeled 11 or 17, etc.

But we don't see the full maze, but likely we're supposed to continue.

Wait — maybe we missed something.

Let’s double-check the start box:

You wrote: 15,40 → you did prime factorization:

```
5 | 15 40
3 8
```

That's correct!

15 ÷ 5 = 3
40 ÷ 5 = 8
So GCF = 5 → ✔️

Then 12,54:

- 12 = 2×2×3
- 54 = 2×3×3×3
- Common: 2×3 = 6 → ✔️

Then 39,26:

- 39 = 3×13
- 26 = 2×13 → GCF = 13 → ✔️

Then 24,64:

- 24 = 2³×3
- 64 = 2⁶ → GCF = 2³ = 8 → ✔️

Now, from 24,64, arrow 8 leads to a box — probably something like 48, 56 or similar.

But since we can't see the rest, perhaps the goal is just to find the GCFs and trace the path.

Alternatively, maybe the answer is just the sequence of GCFs along the path.

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✔ Final Answer: The Correct Path and GCFs

| Box | Numbers | GCF | Next Step |
|-----|--------|-----|-----------|
| Start | 15, 40 | 5 | → 12, 54 |
| 12, 54 | 12, 54 | 6 | → 39, 26 |
| 39, 26 | 39, 26 | 13 | → 24, 64 |
| 24, 64 | 24, 64 | 8 | → ??? |

So the path is determined by these GCFs:
👉 5 → 6 → 13 → 8

And the correct route follows those numbers.

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📌 Summary

To solve the maze:

1. Find GCF of each pair
2. Follow the arrow labeled with that GCF
3. Continue until exit

You've already correctly computed:
- GCF(15,40) = 5 → ✔️
- Then proceed to 12,54 → GCF = 6
- Then to 39,26 → GCF = 13
- Then to 24,64 → GCF = 8

✔ So your solution is on the right track.

If the maze ends at 24,64, then the final answer is 8.

Or if it continues, keep applying the same method.

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🔍 Extra: What about other boxes?

Just to be thorough:

- 35, 28: GCF = 7
- 50, 40: GCF = 10 (since 50=2×5², 40=2³×5 → GCF = 2×5 = 10)
- But we don’t use them because they’re not on the path from GCF=5.

So only the path with GCFs 5→6→13→8 is valid.

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✔ Final Answer:

The correct path uses these GCFs:
> 5 → 6 → 13 → 8

And you’ve started correctly! Keep following the GCF values to navigate the maze.

Let me know if you want help finishing the entire maze or solving the next steps!