Question

Total number of prime factors of ((7*2)^24) *(4*5)^21= ?

Answer 1

Answer:

(7 * 2)^24 * (4 * 5)^21.

= (7 )^24 * (2)^24 * ((2)^21 * (2) * 21) * (5)^21 we just splited 4 to 2 * 2.

= (7 )^24 * ((2)^24 + 21+21) * (5)^21.

= ((7 )^24 * (2)^66 (5)^21.

= 24 + 66 + 21 = 111.

Step-by-step explanation:

Answer 2

The total number of prime factors of the given number is three.

Given:

((7*2)^24) *(4*5)^21

To Find:

The total number of prime factors.

Solution:

To find the total number of prime factors. We have to show the given number only in terms of prime numbers.

((7*2)^24) *(4*5)^21

= 7^24 *2^24 *(2*2*5)^21

= 7^24 * 2^24 * 2^21*2^21*5^21

= 7^24 * 2^(24+21+21) * 5^21

=  7^24 * 2^66 * 5^21

2, 5, and 7 are prime numbers.

∴ The total number of prime factors of the given number is three.

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