Question

2. Determine the prime factorization of each number. a) 95 b) 112 c) 164 d) 150​

Answer 1

Answer:

In explanation.

Step-by-step explanation:

A). 95 = 51 × 191 where 5, 19 are prime.

-The prime factors of 96 thus obtained are written as 96 = 2 × 2 × 2 × 2 × 2 × 3 = 25 × 31, where 2 and 3 are the prime numbers.

B). 112 = Dividing 112 by 56, we get 112 ÷ 56 = 2. Thus the prime factorization of 112 = 2 x 2 x 2 x 2 x 7 is obtained by writing the factor tree of 112.

-112  is a composite number. 112 = 1 x 112, 2 x 56, 4 x 28, 7 x 16, or 8 x 14.

-Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112.

-Prime factorization: 112 = 2 x 2 x 2 x 2 x 7, which can also be written 112 = 2⁴ x 7.

C). 164 = The prime factorization of 164 can be written as 22 × 411 where 2, 41 are prime.

-The prime factors of 165 are 3, 5, 11. Therefore, the product of prime factors = 3 × 5 × 11 = 165.

D). 150 = Prime Factorization of 150: 2 × 3 × 52

-The prime factorization of 150 is 2 x 3 x 5 x 5 = 2 x 3 × 52 where 2, 3, and 5 are the prime numbers.