SAMs

Number Theory Level 2

How many positive integer divisors does 3 , 000 , 000 3,000,000 have?

3,000,000 98 3001 100

Ziyong Cui by Ziyong Cui , 29, USA

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2 solutions

Natsir Muhammad
Jun 26, 2014

well, we know that 3,000,000 = 3^1 x 2^6 x 5 ^6 then positive integer divisors = (1+1) x (6+1) x (6+1) = 98 yeah :)

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is there any particular logic behind this?

Wrik Bhadra - 6 years, 5 months ago

To calculate the divisors of a number,factor that number,add one to each of the exponents and multiply them together. 3 , 000 , 000 = 3 1 × 2 6 × 5 6 3,000,000=3^1\times2^6\times5^6 so ( 1 + 1 ) ( 6 + 1 ) ( 6 + 1 ) = 2 × 7 × 7 = 2 × 49 = 98 (1+1)(6+1)(6+1)=2\times7\times7=2\times49=\boxed{98}

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