Explanation:
We need to write the prime factorization of each number — that means breaking it down into a product of prime numbers only.
Let’s go one by one, checking divisibility starting with the smallest prime (2), then 3, 5, 7, etc., until we get only primes.
1) 33
- 33 ÷ 3 = 11 → both 3 and 11 are prime.
→ 33 = 3 × 11
2) 25
- 25 ÷ 5 = 5 → 5 is prime.
→ 25 = 5 × 5 = 5²
3) 14
- 14 ÷ 2 = 7 → 2 and 7 are prime.
→ 14 = 2 × 7
4) 8
- 8 ÷ 2 = 4
- 4 ÷ 2 = 2
- 2 ÷ 2 = 1
→ 8 = 2 × 2 × 2 = 2³
5) 20
- 20 ÷ 2 = 10
- 10 ÷ 2 = 5
→ 20 = 2 × 2 × 5 = 2² × 5
6) 30
- 30 ÷ 2 = 15
- 15 ÷ 3 = 5
→ 30 = 2 × 3 × 5
7) 18
- 18 ÷ 2 = 9
- 9 ÷ 3 = 3
→ 18 = 2 × 3 × 3 = 2 × 3²
8) 24
- 24 ÷ 2 = 12
- 12 ÷ 2 = 6
- 6 ÷ 2 = 3
→ 24 = 2 × 2 × 2 × 3 = 2³ × 3
9) 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
→ 27 = 3 × 3 × 3 = 3³
10) 44
- 44 ÷ 2 = 22
- 22 ÷ 2 = 11
→ 44 = 2 × 2 × 11 = 2² × 11
11) 50
- 50 ÷ 2 = 25
- 25 ÷ 5 = 5
→ 50 = 2 × 5 × 5 = 2 × 5²
12) 35
- 35 ÷ 5 = 7
→ 35 = 5 × 7
13) 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
→ 45 = 3 × 3 × 5 = 3² × 5
14) 60
- 60 ÷ 2 = 30
- 30 ÷ 2 = 15
- 15 ÷ 3 = 5
→ 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5
15) 32
- 32 ÷ 2 = 16
- 16 ÷ 2 = 8
- 8 ÷ 2 = 4
- 4 ÷ 2 = 2
→ 32 = 2⁵
16) 42
- 42 ÷ 2 = 21
- 21 ÷ 3 = 7
→ 42 = 2 × 3 × 7
17) 48
- 48 ÷ 2 = 24
- 24 ÷ 2 = 12
- 12 ÷ 2 = 6
- 6 ÷ 2 = 3
→ 48 = 2⁴ × 3
18) 54
- 54 ÷ 2 = 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
→ 54 = 2 × 3 × 3 × 3 = 2 × 3³
19) 36
- 36 ÷ 2 = 18
- 18 ÷ 2 = 9
- 9 ÷ 3 = 3
→ 36 = 2 × 2 × 3 × 3 = 2² × 3²
20) 80
- 80 ÷ 2 = 40
- 40 ÷ 2 = 20
- 20 ÷ 2 = 10
- 10 ÷ 2 = 5
→ 80 = 2⁴ × 5
Now double-check a few to be safe:
- 33 = 3×11 ✔️
- 25 = 5×5 ✔️
- 80 = 16×5 = 2⁴×5 ✔️
All look correct.
Final Answer:
1) 33 = 3 × 11
2) 25 = 5 × 5
3) 14 = 2 × 7
4) 8 = 2 × 2 × 2
5) 20 = 2 × 2 × 5
6) 30 = 2 × 3 × 5
7) 18 = 2 × 3 × 3
8) 24 = 2 × 2 × 2 × 3
9) 27 = 3 × 3 × 3
10) 44 = 2 × 2 × 11
11) 50 = 2 × 5 × 5
12) 35 = 5 × 7
13) 45 = 3 × 3 × 5
14) 60 = 2 × 2 × 3 × 5
15) 32 = 2 × 2 × 2 × 2 × 2
16) 42 = 2 × 3 × 7
17) 48 = 2 × 2 × 2 × 2 × 3
18) 54 = 2 × 3 × 3 × 3
19) 36 = 2 × 2 × 3 × 3
20) 80 = 2 × 2 × 2 × 2 × 5
Parent Tip: Review the logic above to help your child master the concept of prime factorization worksheet for 5th grade.
