Question

The exponent of 2 in the prime factorisation of 144, is
(a) 4
(b) 5
(c) 6
(d) 3

Answer 1

Option (a) is Correct : 4

The exponent of 2 in the prime factorisation of 144, is 4 .

SOLUTION :  

To express 144 as a product of its prime factors from a factor tree.

Given number : 144

Then, factor tree of 144 is given in the ATTACHMENT.  

Therefore , 144 = 2 × 2 × 2 × 2 × 3 × 3 = 2⁴ × 3²

Hence, the exponent of 2  the prime factorization  of  144  is 2⁴ .  

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Answer 2

The method in which we multiply prime numbers in order to make original number is called as prime factorization.

(1)

Prime factorization of 144 = 2 * 2 * 2 * 2 * 3 * 3.

⇒ 2⁴ * 3².

Therefore, exponent of 2 is 4.

The answer is Option(A).

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