Question

The number of prime factors of (3 x 5)^12 (2 x 7)^10 (10)^25 is

Answer 1

(3 × 5)^12 (2 × 7)^10 (10)^25
= (3^12) (5^12) (2^10) (7^10) (2 × 5)^25
= (2^10. 2^25) (3^12) (5^12. 5^25) (7^10)
= 2^35 . 3^12 . 5^37 . 7^10
Reqd. prime factors are :
2^35 . 3^12 . 5^37 . 7^10

Answer 2

Answer:

4 prime factors - 2,3,5,7

Step-by-step explanation:

Given : Expression $(3\times 5)^{12}(2\times 7)^{10}(10)^{25}$

To find : The number of prime factors of expression ?

Solution :

Re-write expression as

$=(3\times 5)^{12}(2\times 7)^{10}(10)^{25}$

$=3^{12}\times 5^{12}\times 2^{10}\times 7^{10}\times (2\times 5)^{25}$

$=3^{12}\times 5^{12}\times 2^{10}\times 7^{10}\times 2^{25}\times 5^{25}$

$=3^{12}\times 5^{12+25}\times 2^{10+25}\times 7^{10}$

$=3^{12}\times 5^{37}\times 2^{35}\times 7^{10}$

Prime factor is the factor that can be multiplied to give original number.

So, prime factors in the expression are 2,3,5,7 i.e. 4 prime factors.