Prime Factorization Worksheets - Math Monks - Free Printable

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

We’ll break down each number into its prime factors first, then group same primes and count how many times they appear — that becomes the exponent.

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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

✔ Check: 2⁴ = 16, 16 × 5 = 80 ✔️

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c) 76

76 ÷ 2 = 38
38 ÷ 2 = 19 → 19 is prime
So: 76 = 2 × 2 × 19 = 2² × 19¹

✔ Check: 4 × 19 = 76 ✔️

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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

✔ Check: 2 × 9 × 5 = 90 ✔️

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e) 20

20 ÷ 2 = 10
10 ÷ 2 = 5 → 5 is prime
So: 20 = 2 × 2 × 5 = 2² × 5¹

✔ Check: 4 × 5 = 20 ✔️

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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

✔ Check: 2⁵ = 32 ✔️

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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

✔ Check: 2 × 27 = 54 ✔️

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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

✔ Check: 8 × 11 = 88 ✔️

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i) 44

44 ÷ 2 = 22
22 ÷ 2 = 11 → 11 is prime
So: 44 = 2 × 2 × 11 = 2² × 11¹

✔ Check: 4 × 11 = 44 ✔️

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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

✔ Check: 8 × 3 × 7 = 24 × 7 = 168 ✔️

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k) 81

81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
All 3s! So: 81 = 3 × 3 × 3 × 3 = 3⁴

✔ Check: 3⁴ = 81 ✔️

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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

✔ Check: 2 × 27 × 5 = 54 × 5 = 270 ✔️

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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