Factor and multiples

Number Theory Level 3

8050755076 has a total amount of $N$ factors (inclusive of 1 and itself).

Determine whether $N$ is odd or even.

Odd Even

2 solutions

Tom Engelsman
Jun 22, 2017

It turns out $8,050,755,076 = (2 \cdot 7 \cdot 13 \cdot 17 \cdot 29)^2 = 2^2 7^2 13^2 17^2 29^2$ , which has $3^5 = 243$ positive integer divisors.

J Park
Mar 5, 2017

You don't need to find every factor. You just need to see if 8,050,755,076 can be square rooted. And it is 89,726.

How almost every number of factors are even is because if you do the factor rainbow, you always put a number in the beginning and at the end. But if you get the same number times same number, you only put the number once. So its like even even even even odds.