Prime Factor Tree worksheet for practicing prime factorization.

Let’s solve each prime factor tree step by step.

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Problem 1: 99

We start with 99. It splits into two parts: one is 9, the other is unknown.

99 ÷ 9 = 11 → So the left circle is 11

Now, 9 splits into two circles. 9 = 3 × 3 → so both circles are 3

Prime factors: 11, 3, 3

Product of prime factors: 3 × 3 × 11 = 99

✔ Correct.

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Problem 2: 36

36 splits into 9 and an unknown box.

36 ÷ 9 = 4 → so the right box is 4

9 splits into 3 and another circle → 9 ÷ 3 = 3 → so that circle is 3

4 splits into two circles: one is 2, so the other is 4 ÷ 2 = 2

Prime factors: 3, 3, 2, 2

Product: 2 × 2 × 3 × 3 = 36

✔ Correct.

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Problem 3: 96

96 splits into 4 and a box.

96 ÷ 4 = 24 → so the right box is 24

4 splits into 2 and a circle → 4 ÷ 2 = 2 → so that circle is 2

24 splits into 2 and a box → 24 ÷ 2 = 12 → so that box is 12

12 splits into 3 and a box → 12 ÷ 3 = 4 → so that box is 4

4 splits into two circles → 4 = 2 × 2 → so both circles are 2

Prime factors: 2, 2, 2, 3, 2, 2 → wait, let’s list them in order from bottom up:

From left branch: 2, 2
From right branch: 2, 3, 2, 2 → actually, better to collect all leaves:

Left side: 2 (from 4), and 2 (other part of 4) → no, wait:

Actually, 4 → 2 and 2
Then 24 → 2 and 12
12 → 3 and 4
4 → 2 and 2

So all prime factors: 2, 2 (from first 4), then 2 (from 24→2), 3 (from 12→3), 2, 2 (from last 4)

That’s six numbers: 2, 2, 2, 3, 2, 2 → but we can group: 2⁵ × 3

Check: 2×2×2×2×2×3 = 32×3 = 96 ✔

Product of prime factors: 2 × 2 × 2 × 2 × 2 × 3 = 96

But for the answer, we write the product as multiplication: 2 × 2 × 2 × 2 × 2 × 3

Or simplified: 2⁵ × 3, but since the worksheet says “product of prime factors”, we write the multiplication.

Actually, looking at the worksheet, it just says “Product of prime factors” — probably expects the multiplication expression or the number? But in context, since they’re filling trees, likely they want the multiplication of the primes found.

But in problem 1, we had 3×3×11=99, so same here.

So: 2 × 2 × 2 × 2 × 2 × 3 = 96

But let’s write it neatly.

Actually, standard way is to list the prime factors multiplied together.

So for 96: 2 × 2 × 2 × 2 × 2 × 3

But we can also write as 2^5 × 3, but since the worksheet doesn’t specify exponent form, and others are written as products, I’ll use multiplication.

Wait, in problem 1, we wrote 3×3×11, which is fine.

Similarly here: 2×2×2×2×2×3

But let’s confirm the tree:

Top: 96
→ left: 4 → 2 and 2
→ right: 24 → 2 and 12 → 12 → 3 and 4 → 4 → 2 and 2

So primes: 2,2,2,3,2,2 → yes, five 2s and one 3.

Product: 2×2×2×2×2×3 = 96

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Problem 4: 48

48 splits into 2 and a box.

48 ÷ 2 = 24 → so the right box is 24

24 splits into 4 and a box.

24 ÷ 4 = 6 → so the right box is 6

4 splits into two circles → 4 = 2 × 2 → so both circles are 2

6 splits into 2 and 3 → already given? Wait, in the diagram:

48 → 2 and [24]
[24] → 4 and [6]
4 → two circles (both 2)
6 → 2 and 3 → yes, given as 2 and 3

So prime factors: from left: 2 (first split), then from 4: 2,2; from 6: 2,3

So all: 2, 2, 2, 2, 3

List: 2 (from 48→2), then 2,2 (from 4), then 2,3 (from 6) → that’s four 2s and one 3.

Check: 2×2×2×2×3 = 16×3=48 ✔

Product: 2 × 2 × 2 × 2 × 3 = 48

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Problem 5: 81

81 splits into 3 and a box.

81 ÷ 3 = 27 → so the right box is 27

27 splits into 9 and a circle.

27 ÷ 9 = 3 → so that circle is 3

9 splits into two circles → 9 = 3 × 3 → so both are 3

Prime factors: 3 (first), 3 (from 27→3), 3,3 (from 9) → so four 3s.

Product: 3 × 3 × 3 × 3 = 81 ✔

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Problem 6: 90

90 splits into 2 and a box.

90 ÷ 2 = 45 → so the right box is 45

45 splits into 3 and a box.

45 ÷ 3 = 15 → so that box is 15

15 splits into a circle and 5.

15 ÷ 5 = 3 → so that circle is 3

Prime factors: 2, 3, 3, 5

Product: 2 × 3 × 3 × 5 = 90 ✔

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Now, compiling all answers:

For each problem, we need to fill the blank boxes and circles, and then write the product of prime factors.

But since the user asked to solve the problem, and the final answer should be the completed factorizations or the products? Looking back, the worksheet says: "Fill the numbers in the factor trees then write the prime factors." and "Product of prime factors" with a line.

Probably, for each, we need to state the product.

But in the context, since it's multiple problems, and the final answer should be comprehensive.

Perhaps list for each problem the product of prime factors.

Since the instruction is to provide the final answer after reasoning, and it's multiple parts, I'll list them.

But let me see the format.

Actually, in the response, I should provide the filled values and the products.

But to keep it clean, since the key output is the product of prime factors for each, and that's what goes on the line.

So:

1) Product: 3 × 3 × 11 = 99
But typically, we write the multiplication expression.

In many worksheets, they expect the expression like 3×3×11 or just the number? But it says "product of prime factors", so likely the expression.

Looking at problem 1: after filling, the primes are 11,3,3 so product is 3×3×11

Similarly.

But to be precise, I'll write for each.

Since the final answer section might expect a single thing, but there are six problems.

I think I need to provide all.

Perhaps the final answer is the set of products.

But let's see.

Another way: perhaps for each problem, the product is the number itself, but that's trivial. No, they want the prime factorization product.

I think it's standard to write the multiplication of the prime factors.

So for clarity:

Problem 1: 3 × 3 × 11
Problem 2: 2 × 2 × 3 × 3
Problem 3: 2 × 2 × 2 × 2 × 2 × 3
Problem 4: 2 × 2 × 2 × 2 × 3
Problem 5: 3 × 3 × 3 × 3
Problem 6: 2 × 3 × 3 × 5

And each equals the original number, but the product expression is what's asked.

In the worksheet, it says "write the prime factors" and "product of prime factors", so likely the expression.

To confirm, in problem 1, if they write 3×3×11, that's fine.

So I'll go with that.

Now, for the final answer, since it's multiple, I'll list them.

But the instruction says "provide only the final correct answer", so perhaps box all.

Since it's a worksheet, maybe present as:

1) 3 × 3 × 11
2) 2 × 2 × 3 × 3
3) 2 × 2 × 2 × 2 × 2 × 3
4) 2 × 2 × 2 × 2 × 3
5) 3 × 3 × 3 × 3
6) 2 × 3 × 3 × 5

Yes.

I could write the products as numbers, but that defeats the purpose; the point is to show the prime factorization.

In the context, "product of prime factors" means the expression multiplying the primes.

So I think this is correct.

Final verification:

1) 99 = 3² × 11 → 3×3×11
2) 36 = 2² × 3² → 2×2×3×3
3) 96 = 2⁵ × 3 → 2×2×2×2×2×3
4) 48 = 2⁴ × 3 → 2×2×2×2×3
5) 81 = 3⁴ → 3×3×3×3
6) 90 = 2 × 3² × 5 → 2×3×3×5

All correct.

So the final answer is the list above.