Let’s solve each number step by step to find its prime factors and write them in exponential form.
---
a) 20 → Already done:
20 ÷ 2 = 10
10 ÷ 2 = 5
5 is prime.
So, 2² × 5¹
✔
---
b) 72
72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
Prime factors: 2, 2, 2, 3, 3 → 2³ × 3²
---
c) 68
68 ÷ 2 = 34
34 ÷ 2 = 17
17 is prime.
So, 2² × 17¹
---
d) 55
55 ÷ 5 = 11
11 is prime.
So, 5¹ × 11¹
---
e) 30
30 ÷ 2 = 15
15 ÷ 3 = 5
5 is prime.
So, 2¹ × 3¹ × 5¹
---
f) 74
74 ÷ 2 = 37
37 is prime.
So, 2¹ × 37¹
---
g) 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 is prime.
So, 3¹ × 5¹ × 7¹
---
h) 198
198 ÷ 2 = 99
99 ÷ 3 = 33
33 ÷ 3 = 11
11 is prime.
So, 2¹ × 3² × 11¹
---
i) 90
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 is prime.
So, 2¹ × 3² × 5¹
---
j) 48
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
3 is prime.
So, 2⁴ × 3¹
---
k) 66
66 ÷ 2 = 33
33 ÷ 3 = 11
11 is prime.
So, 2¹ × 3¹ × 11¹
---
l) 68 → Same as (c):
68 ÷ 2 = 34
34 ÷ 2 = 17
17 is prime.
So, 2² × 17¹
---
m) 42
42 ÷ 2 = 21
21 ÷ 3 = 7
7 is prime.
So, 2¹ × 3¹ × 7¹
---
n) 39
39 ÷ 3 = 13
13 is prime.
So, 3¹ × 13¹
---
o) 21
21 ÷ 3 = 7
7 is prime.
So, 3¹ × 7¹
---
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
Parent Tip: Review the logic above to help your child master the concept of 6th grade factor tree worksheet on math.
