# The sum of the exponents of the prime factors in the prime factorisation of 196,

Question:

The sum of the exponents of the prime factors in the prime factorisation of 196, is

(a) 1

(b) 2

(c) 4

(d) 6

Solution:

Using the factor tree for prime factorization, we have:

Therefore,

$196=2 \times 2 \times 7 \times 7$

$196=2^{2} \times 7^{2}$

The exponents of 2 and 7 are 2 and 2 respectively.

Thus the sum of the exponents is 4

Hence the correct choice is (c).