If $6370=2^m.5^n.7^k.13^p$, then find $m+n+k+p$.

Given :

The given expression is $6370 = 2^m . 5^n . 7^k . 13^p$.

To do :

We have to find the value of $m + n + k + p$.

Solution :

Factorisation of 6370 is,

         2 | 6370

       __|______
         5 | 3185

       __|______

         7 | 637

       __|______

         7 | 91

       __|______

               13       

$6370 = 2 \times 5 \times 7 \times 7 \times 13$

           $= 2 \times 5 \times 7^2 \times 13$

It is given that, $6370 = 2^m . 5^n . 7^k . 13^p$

On comparing, 

$ 2^m . 5^n . 7^k . 13^p = 2 \times 5 \times 7^2 \times 13$

$m = 1$

$n = 1$

$k = 2$

$p = 1$

$m + n + k + p =  1 + 1 + 2 + 1$

$m + n + k + p = 5$.

Therefore, the value of $m + n + k + p$ is 5

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Updated on: 10-Oct-2022

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