Question

find the highest common factor by prime factorization method
a.84,96
b.60,75​

Answer 1

Answer:

a) Prime factorization of 84 is 2 × 2 × 3 × 7

Prime factorization of 96 is 2 × 2 × 2 × 2 × 2 × 3

The common factor in the prime factorization of 84 and 96 are 2, 2, and 3.

b) prime factorization of 60 = 2 × 2 × 3 × 5

Prime factorization of 75 = 5 × 5 × 3

The common factors in the prime factorization of 60 and 75 are 3 and 5

Answer 2

(a)Ans=12

The prime factorization of 84 is: 2 x 2 x 3 x 7. The prime factorization of 96 is: 2 x 2 x 2 x 2 x 2 x 3. The prime factors and multiplicities 84 and 96 have in common are: 2 x 2 x 3. 2 x 2 x 3 is the gcf of 84 and 96.

(b)Ans=15

The prime factorization of 60 is: 2 x 2 x 3 x 5. The prime factorization of 75 is: 3 x 5 x 5. The prime factors and multiplicities 60 and 75 have in common are: 3 x 5. 3 x 5 is the gcf of 60 and 75