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

Office Hours

On December 20, 2023, Brent will stop offering office hours. 

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Have a question about this video?

Post your question in the Comment section below, and a GMAT expert will answer it as fast as humanly possible.

Free “Question of the Day” emails!