Question

Find the sum of exponent of prime factors in the factorisation of 31500

Answer 1

Sum of exponents = 2+2+3+1=8

Answer 2

The sum of exponent of prime factors in the factorization of 31500  is 8 .

Explanation:

The factorization of 31500 = 315 x 100

= (63 x 5) x (10 x 10)

= (9 x 7 )x 5 x (5 x 2) x (5 x 2)

= (3 x 3) x 7 x 5 x 5 x 2 x 5 x 2

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

So , the prime factors in the factorization of 31500 = $3\times3\times7\times5\times5\times5\times2\times2$

$=3^2\times5^3\times7^1\times2^2$

Now , the sum of exponent of prime factors in the factorisation of 31500 would be (2)+(3)+(1)+(2)=2+3+1+2= 8

Hence, the sum of exponent of prime factors in the factorisation of 31500  is 8 .

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