A number theory problem by Andrea Palma

Number Theory Level 2

Find the sum all the positive divisors of 56.

The answer is 120.

1 solution

Rishabh Jain
Feb 22, 2016

$\Large 56=2^3\times 7$ Note that sum of all its divisors( total 8) can be written as : $\Large (2^0+2^1+2^2+2^3)(7^0+7^1)$ $\huge =\boxed{\color{#007fff}{120}}$

Nice trick, did not know that before

Adrian Ma - 8 months ago

...... Why not the answer is 14? 2×2×2×7×1 so sum of divisors = 14.

Atanu Ghosh - 5 years, 3 months ago

2x2x2x7 is the unique (up to order) prime factorisation of 56 whereas this question is asking about all positive divisors (factors) that is 1,2,4,7,8,14,28,56.

Chris Cooper - 5 years, 3 months ago

Thanks, you are right and i am wrong. Again thankyou very much for correcting my mistake.

Atanu Ghosh - 5 years, 3 months ago

@Atanu Ghosh Your solution is incomplete. For instance, 4 is also a divisor of 56. Have you considered that?

Pulkit Gupta - 5 years, 3 months ago

A number theory problem by Andrea Palma

The answer is 120.

1 solution

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