Question

The product of all factors of number N is equal to the tenth power of the number. which of the following cannot be a factor of N?
a. 90
b. 210
c. 126
d. 135
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Answer 1

Answer:

i think its c. 126

Step-by-step explanation:

please comment my answer if its correct or not.

Answer 2

Answer:

210 cannot be the factor of the number N.

Step-by-step explanation:

Let the number of factors of number N be x.

Then the product of the factors of number N$=N^{x/2}$

Given that the product of all factors is equal to the tenth power of the number, $\implies N^{x/2} =N^{10}$

$\implies x/2 =10\implies x=20$

Now 20 can be expressed as $1*20, 2*10, 4*5,2*2*5$

So, $4*5=a^{3} *b$ $2*2*5=a*b*c$ where a, b, c are prime numbers.

So amongst the given numbers, only 210 cannot be expressed using the factors of N.

Therefore, 210 cannot be the factor of N.