[short solution] Find the sum of exponents of prime factorisation of 196 ?

[short solution] Find the sum of exponents of prime factorisation of 196 ?

Aditya Raj Anand

Wednesday 27 October 2021

math

Find the sum of exponents of prime factorisation of 196?

Let's first calculate the prime factorization of 196.

Now, 

1. Divide 196 by 2 the results will be 98.

2. Again divide 98 by 2, the results will be 49.

3. Now, divide 49 by 7, the result will be 7.

4. At last divide 7 by 7, the result will be 1.

Hence, the prime factorization has been completed because the end result after division is 1.

Therefore, the prime factorization of 196 will be like this:

196 = 2 × 2 × 7 × 7

196 = 2² × 7²

Here the exponent or power of the prime factorization of 196 is 2 and 2. Now, if we add these numbers, the answer will be 4. Therefore, the sum of the exponent of the prime factorization of 196 is 4.