A number theory problem by Ajay Sutradhar

Number Theory Level 3

How many positive factors does the above number have?

The answer is 1030301.

2 solutions

William Isoroku
Dec 26, 2014

Prime factorization of ${30}^{100}$ is ${3}^{100}\cdot{2}^{100}\cdot{5}^{100}$

By Euler's theorem of positive divisors, add $1$ to every exponent in the prime factored form and multiply them: $(100+1)\cdot(100+1)\cdot(100+1)$ which is $\boxed{1030301}$

Ajay Sutradhar
Sep 29, 2014

30=2x5x3

therefore the factors of the given number is (100+1)(100+1)(100+1)

Ie, 1030301

Sorry, but this is wrong. With this you only get all positive factors. You need to add the number of all negative factors as well. So the actually answer is $2 * 101^{3} = 2 * 1030301 =\boxed{2060602}$

Patrick Engelmann - 6 years, 8 months ago

Thanks. I have added "positive" to the question.

Those who previously answered 2060602 have been marked correct.

Calvin Lin Staff - 6 years, 8 months ago

A number theory problem by Ajay Sutradhar

The answer is 1030301.

2 solutions

0 pending reports