How many factors does the positive integer 180 have?

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Official Explanation

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To determine the number of factors of the integer 180, we first perform its prime factorization. The prime factorization of 180 is

180=2^2*3^2*5^1

. Using the formula for finding the number of factors, which is…

Comments

ArjunSep 17, 2024

can you explain more?

MuhammadJul 4, 2024

thank you for sharing

PratyushMay 6

Wait, why do we add 1 to each exponent? I keep getting 18 but not sure if that's by luck lol

MarcoMay 10

it's because each factor can use 0 up to the full exponent of a prime, so you get (exp+1) choices for each one

NathanMay 19

ohh that makes sense, thanks!

What this question tests

Your command of divisibility, primes, factors, parity, and how the GMAT tests properties of integers.

Forgetting that 1 is not prime, that 0 is divisible by every integer, or that negative numbers flip your assumptions.