Prime Factorization Worksheets - Math Monks - Free Printable

Let’s solve each problem step by step. We need to find the prime factorization of each number and write it in exponential form — that means writing repeated prime factors as powers (like 2² instead of 2 × 2).

We’ll go one by one:

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b) 72

Start dividing by smallest primes:

72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

So, 72 = 2 × 2 × 2 × 3 × 3 → 2³ × 3²

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c) 68

68 ÷ 2 = 34
34 ÷ 2 = 17
17 is prime.

So, 68 = 2 × 2 × 17 → 2² × 17¹

*(Note: Usually we don’t write the exponent if it’s 1, but since the example wrote 5¹, we’ll follow that style.)*

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d) 55

55 ÷ 5 = 11
11 is prime.

So, 55 = 5 × 11 → 5¹ × 11¹

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e) 30

30 ÷ 2 = 15
15 ÷ 3 = 5
5 is prime.

So, 30 = 2 × 3 × 5 → 2¹ × 3¹ × 5¹

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f) 74

74 ÷ 2 = 37
37 is prime.

So, 74 = 2 × 37 → 2¹ × 37¹

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g) 105

105 ÷ 3 = 35
35 ÷ 5 = 7
7 is prime.

So, 105 = 3 × 5 × 7 → 3¹ × 5¹ × 7¹

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h) 198

198 ÷ 2 = 99
99 ÷ 3 = 33
33 ÷ 3 = 11
11 is prime.

So, 198 = 2 × 3 × 3 × 11 → 2¹ × 3² × 11¹

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i) 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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j) 48

48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
3 is prime.

So, 48 = 2 × 2 × 2 × 2 × 3 → 2⁴ × 3¹

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k) 66

66 ÷ 2 = 33
33 ÷ 3 = 11
11 is prime.

So, 66 = 2 × 3 × 11 → 2¹ × 3¹ × 11¹

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l) 68 ← Same as part c!

Already done: 2² × 17¹

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m) 42

42 ÷ 2 = 21
21 ÷ 3 = 7
7 is prime.

So, 42 = 2 × 3 × 7 → 2¹ × 3¹ × 7¹

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n) 39

39 ÷ 3 = 13
13 is prime.

So, 39 = 3 × 13 → 3¹ × 13¹

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o) 21

21 ÷ 3 = 7
7 is prime.

So, 21 = 3 × 7 → 3¹ × 7¹

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✔ All calculations checked. Now here are the final answers in order:

Final Answer:
b) 2³ × 3²
c) 2² × 17¹
d) 5¹ × 11¹
e) 2¹ × 3¹ × 5¹
f) 2¹ × 37¹
g) 3¹ × 5¹ × 7¹
h) 2¹ × 3² × 11¹
i) 2¹ × 3² × 5¹
j) 2⁴ × 3¹
k) 2¹ × 3¹ × 11¹
l) 2² × 17¹
m) 2¹ × 3¹ × 7¹
n) 3¹ × 13¹
o) 3¹ × 7¹