Prime Factorization Worksheets - Math Monks - Free Printable

Let’s solve each problem step by step. We need to break down each number into its prime factors, then write them using exponents (like in the example: 48 = 2⁴ × 3¹).

We’ll go one by one:

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b) 80

Start dividing by smallest prime: 2
80 ÷ 2 = 40
40 ÷ 2 = 20
20 ÷ 2 = 10
10 ÷ 2 = 5 → now 5 is prime.

So: 80 = 2 × 2 × 2 × 2 × 5 = 2⁴ × 5¹

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c) 76

76 ÷ 2 = 38
38 ÷ 2 = 19 → 19 is prime.

So: 76 = 2 × 2 × 19 = 2² × 19¹

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d) 90

90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5 → 5 is prime.

So: 90 = 2 × 3 × 3 × 5 = 2¹ × 3² × 5¹

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e) 20

20 ÷ 2 = 10
10 ÷ 2 = 5 → 5 is prime.

So: 20 = 2 × 2 × 5 = 2² × 5¹

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f) 32

32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1

All 2s! So: 32 = 2 × 2 × 2 × 2 × 2 = 2⁵

(We can write it as 2⁵ × 1, but usually we just say 2⁵ — but since the example wrote 3¹, let’s be consistent and include exponent 1 if needed. But 32 has only factor 2, so 2⁵ is fine.)

Actually, looking at the example: they wrote 2⁴·3¹ — so even if exponent is 1, they wrote it. So for consistency, we’ll do same.

But 32 = 2⁵ — no other primes. So we can write 2⁵ or 2⁵ × 1, but 1 isn’t a prime. So best to just write 2⁵.

Wait — actually, in math, when there’s only one prime factor, we don’t multiply by anything else. The example had two different primes. So for 32, it’s just 2⁵.

But let’s check instructions: “write in exponent form” — like the example. Example included both primes with exponents. For numbers with only one prime, we just write that prime to its power.

So 32 = 2⁵

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g) 54

54 ÷ 2 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

So: 54 = 2 × 3 × 3 × 3 = 2¹ × 3³

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h) 88

88 ÷ 2 = 44
44 ÷ 2 = 22
22 ÷ 2 = 11 → 11 is prime.

So: 88 = 2 × 2 × 2 × 11 = 2³ × 11¹

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i) 44

44 ÷ 2 = 22
22 ÷ 2 = 11 → 11 is prime.

So: 44 = 2 × 2 × 11 = 2² × 11¹

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j) 168

168 ÷ 2 = 84
84 ÷ 2 = 42
42 ÷ 2 = 21
21 ÷ 3 = 7 → 7 is prime.

So: 168 = 2 × 2 × 2 × 3 × 7 = 2³ × 3¹ × 7¹

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k) 81

81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

All 3s: 81 = 3 × 3 × 3 × 3 = 3⁴

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l) 270

270 ÷ 2 = 135
135 ÷ 3 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5 → 5 is prime.

So: 270 = 2 × 3 × 3 × 3 × 5 = 2¹ × 3³ × 5¹

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Now let’s double-check a few to make sure:

- 80: 2⁴=16, 16×5=80 ✔
- 76: 2²=4, 4×19=76 ✔
- 90: 2×9×5=90 ✔
- 20: 4×5=20 ✔
- 32: 2⁵=32 ✔
- 54: 2×27=54 ✔
- 88: 8×11=88 ✔
- 44: 4×11=44 ✔
- 168: 8×3×7=168 ✔
- 81: 3⁴=81 ✔
- 270: 2×27×5=270 ✔

All correct!

Final Answer:
b) 80 = 2⁴ × 5¹
c) 76 = 2² × 19¹
d) 90 = 2¹ × 3² × 5¹
e) 20 = 2² × 5¹
f) 32 = 2⁵
g) 54 = 2¹ × 3³
h) 88 = 2³ × 11¹
i) 44 = 2² × 11¹
j) 168 = 2³ × 3¹ × 7¹
k) 81 = 3⁴
l) 270 = 2¹ × 3³ × 5¹