What is the highest possible length of an integer that is less than 500? (The length of an integer refers to the total count of prime factors in its prime factorization.)

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Official Explanation

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To determine the maximum length of an integer less than 500, we need to understand that the length is defined as the total number of prime factors, including repetitions, in its prime factorization. The integer 2^8 = 256 is less than 500 and has a length of eight, as it consists…

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Comments

IfeanyichukwuOct 28, 2024

thank you very much!

pranavFeb 23, 2024

thanksss

CallanApr 25

Wait, is "length" the same as the number of prime factors with multiplicity? Like 8 = 2*2*2 counts as 3?

JoãoApr 27

yeah, total count including repeats. that's how i read it too

NiyaApr 26

ok thanks, that changes everything lol

ZenithAug 21

This one tripped me up because I kept thinking distinct primes. Once you allow repeats it's way more doable.

SherveerApr 14

thanks, helpful!

What this question tests

What it tests

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

Common trap

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