Divisors!

Number Theory Level 2

How many positive divisors does 1004006004001 1004006004001 have?

Hint: 1 1 4 11^{4} = = 14641 14641


The answer is 125.

Micah Gadbois by Micah Gadbois , 15, USA

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1 solution

Micah Gadbois
Jul 18, 2017

The prime factorization of 1004006004001 1004006004001 is 7 4 7^4 X 1 1 4 11^4 X 1 3 4 13^4

Add 1 1 to each exponent. Multiply: ( 4 + 1 ) (4+1) X ( 4 + 1 ) (4+1) X ( 4 + 1 ) (4+1) = = 125

1 Helpful 0 Interesting 0 Brilliant 0 Confused

It is extremely hard to find the prime factorisation of a number (think RSA encrytion using 200-digit primes) without searching it up, and I think this distracts from the focus of the question - to use a number's prime factorisation to find its number of divisors. Can you edit your question to include the prime factorisation?

Toby M - 3 years, 10 months ago

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