Question

find the sum of exponents of the prime factors of 156​

Answer 1

156=2×2×3×13

2^2 ×3×13

Sum of exponent = 2+1+1

= 4

Answer 2

The sum of exponents of the prime factors of 156 is 4

Given :

The number 156

To find :

The sum of exponents of the prime factors of 156

Solution :

Step 1 of 2 :

Prime factorise the given number

Here the given number is 156

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:156 \:\:}}}\\ {\underline{\sf{2}}}&\underline{\sf{\:\:78 \:\:}} \\ {\underline{\sf{3}}}&\underline{\sf{\:\:39 \:\:}} \\\underline{\sf{13}}&\underline{\sf{\:\:13\:\:}}\\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

$\displaystyle \sf \therefore \: 156 = 2 \times 2 \times 3 \times 13$

$\displaystyle \sf{ \implies }156 = {2}^{2} \times {3}^{1} \times {13}^{1}$

Step 2 of 2 :

The sum of exponents of the prime factors of 156

$\displaystyle \sf 156 = {2}^{2} \times {3}^{1} \times {13}^{1}$

From prime factorisation of 156 we observe that prime factors of 156 are 2 , 3 and 13.

Exponent of 2 = 2

Exponent of 3 = 1

Exponent of 13 = 1

Hence the sum of exponents of the prime factors of 156

= 2 + 1 + 1

= 4

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