Question

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

Answer 1

Given, (3 x 5)12 (2 x 7)10 (10)25 

= 3 x 5 x 12 x 2 x 7 x 10 x 10 x 25 

= 3 x 5 x 3 x 2 x 2 x 2 x 7 x 2 x 5 x 2 x 5 x 5 x 5 

= 2^5 x 3^2 x 5^5 x 7

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.