Question: Prime Divisors

Comment on Prime Divisors

Hey Brent,

Why dont we consider 1 also to be one of the prime factors of 8500 along with 2,5 and 17.
gmat-admin's picture

1 isn't a prime number.

From the Official Guide: "A prime number is a positive integer that has exactly TWO different positive divisors, 1 and itself."

1 has only one positive divisor, so it is not prime.

My Bad. Thanks for reminding! :D

Would total number of prime factors be 6?
gmat-admin's picture

Good question.
Yes, without the word "DIFFERENT," there would be 6 primes in the factorization of 8500.

Cheers,
Brent

Hi Brent,

What questions can be answered wrongly if we don't include 1 into consideration?

Thank you in advance,
gmat-admin's picture

If you don't include 1 as a divisor (aka factor) of a positive integer, then you risk incorrectly solving questions involving the divisors of numbers.

Consider this Data Sufficiency (partial) question:

What is the value of positive integer n?
Statement 1: n has exactly one positive divisor.

If you don't consider 1 as a given divisor of n, then you'll (incorrectly) conclude that statement 1 is insufficient, since n could equal 2 or 3 or 5, etc

Cheers,
Brent

Hi Brent,

This is a very useful insight,

Thank you very much

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