Using the Factor Tree Method, find the prime factorization of the following:(a) 8(b) 20(c) 34(d) 44(e) 21(f) 42(g) 38(h) 45

To find the prime factorization of each number using the factor tree method, we break down each number into its prime factors. Here’s how you can do it step by step for each number:

(a) 8:

8 is an even number, so divide by 2: 8 ÷ 2 = 4.
4 is still even, divide by 2 again: 4 ÷ 2 = 2.
2 is prime, so we stop here.
Prime factorization: 2 × 2 × 2 = 2³.
(b) 20:

20 is even, divide by 2: 20 ÷ 2 = 10.
10 is even, divide by 2 again: 10 ÷ 2 = 5.
5 is prime, so we stop here.
Prime factorization: 2 × 2 × 5 = 2² × 5.
(c) 34:

34 is even, divide by 2: 34 ÷ 2 = 17.
17 is prime, so we stop here.
Prime factorization: 2 × 17.
(d) 44:

44 is even, divide by 2: 44 ÷ 2 = 22.
22 is even, divide by 2 again: 22 ÷ 2 = 11.
11 is prime, so we stop here.
Prime factorization: 2 × 2 × 11 = 2² × 11.
(e) 21:

21 is odd, so divide by 3: 21 ÷ 3 = 7.
7 is prime, so we stop here.
Prime factorization: 3 × 7.
(f) 42:

42 is even, divide by 2: 42 ÷ 2 = 21.
21 is odd, divide by 3: 21 ÷ 3 = 7.
7 is prime, so we stop here.
Prime factorization: 2 × 3 × 7.
(g) 38:

38 is even, divide by 2: 38 ÷ 2 = 19.
19 is prime, so we stop here.
Prime factorization: 2 × 19.
(h) 45:

45 is odd, divide by 3: 45 ÷ 3 = 15.
15 is odd, divide by 3 again: 15 ÷ 3 = 5.
5 is prime, so we stop here.
Prime factorization: 3 × 3 × 5 = 3² × 5.
Summary of Prime Factorizations: (a) 8 = 2³
(b) 20 = 2² × 5
(c) 34 = 2 × 17
(d) 44 = 2² × 11
(e) 21 = 3 × 7
(f) 42 = 2 × 3 × 7
(g) 38 = 2 × 19
(h) 45 = 3² × 5