Explanation:
We need to find the
prime factorization of each number and write it in
exponential form, like the example:
20 = 2² × 5¹ → written as
2²·5¹
Let’s go one by one, breaking each number into prime factors using division by smallest primes (2, 3, 5, 7, 11, etc.).
---
b) 72
72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
So: 72 = 2 × 2 × 2 × 3 × 3 =
2³·3²
---
c) 68
68 ÷ 2 = 34
34 ÷ 2 = 17
17 is prime.
So: 68 = 2 × 2 × 17 =
2²·17¹
---
d) 55
55 ÷ 5 = 11
11 is prime.
So: 55 = 5 × 11 =
5¹·11¹
---
e) 30
30 ÷ 2 = 15
15 ÷ 3 = 5
5 is prime.
So: 30 = 2 × 3 × 5 =
2¹·3¹·5¹
---
f) 74
74 ÷ 2 = 37
37 is prime.
So: 74 = 2 × 37 =
2¹·37¹
---
g) 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 is prime.
So: 105 = 3 × 5 × 7 =
3¹·5¹·7¹
---
h) 198
198 ÷ 2 = 99
99 ÷ 3 = 33
33 ÷ 3 = 11
11 is prime.
So: 198 = 2 × 3 × 3 × 11 =
2¹·3²·11¹
---
i) 90
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 is prime.
So: 90 = 2 × 3 × 3 × 5 =
2¹·3²·5¹
---
j) 48
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1
So: 48 = 2⁴ × 3 =
2⁴·3¹
---
k) 66
66 ÷ 2 = 33
33 ÷ 3 = 11
11 is prime.
So: 66 = 2 × 3 × 11 =
2¹·3¹·11¹
---
l) 68 — same as part c
→
2²·17¹
---
m) 42
42 ÷ 2 = 21
21 ÷ 3 = 7
7 is prime.
So: 42 = 2 × 3 × 7 =
2¹·3¹·7¹
---
n) 39
39 ÷ 3 = 13
13 is prime.
So: 39 = 3 × 13 =
3¹·13¹
---
o) 21
21 ÷ 3 = 7
7 is prime.
So: 21 = 3 × 7 =
3¹·7¹
Let me double-check each for errors:
- 72 = 2³·3² → 8×9 = 72
✔
- 68 = 4×17 = 68
✔
- 55 = 5×11 = 55
✔
- 30 = 2×3×5 = 30
✔
- 74 = 2×37 = 74
✔
- 105 = 3×5×7 = 105
✔
- 198 = 2×9×11 = 198
✔
- 90 = 2×9×5 = 90
✔
- 48 = 16×3 = 48
✔
- 66 = 2×3×11 = 66
✔
- 42 = 2×3×7 = 42
✔
- 39 = 3×13 = 39
✔
- 21 = 3×7 = 21
✔
All correct.
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 prime factorization worksheet 7th grade.
