Prime factors

Number Theory Level 2

A number N when factorised can be written $N = a^{4} \times b^{3} \times c^{7}$ . Find the number of perfect squares which are factors of N (the three prime numbers a,b,c>2)

The answer is 24.

1 solution

Rubal Singh Dhaliwal
Sep 12, 2017

In order that perfect square divides N, the powers of "a" can be 0,2,4 i.e. (3). Powers of "b" can be 0,2, i.e. (2). Power of "c" can be 0,2,4,6 i.e. (4)

Hence, a combination of these powers given $\Rightarrow 3 \times 2 \times 4. \Longrightarrow i.e. 24$ numbers

Prime factors

The answer is 24.

1 solution

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