# SAT Math: Arithmetic

## Factors

If x = 60, how many distinct prime factors does x have?

A.   0

B.   2

C.   3

D.   4

E.   5

## Knowsys Method

Read the question carefully.  You will want to use a different method for finding the prime factors of a problem than you would use to find all of the factors.  The word "distinct" is also important; you are looking for different prime numbers.

Identify the bottom line. How many distinct prime factors of 60 are there?

Assess your options.  Use a factor tree to quickly solve this problem.  Remember, it doesn't matter how you break down the number 60, the result will always contain the same numbers.

Attack the problem.  Divide 60 by any number to begin your factor tree.  Keep dividing each number until it is no longer divisible by anything except itself and one.  Two possible trees are given below.  Notice that they both contain the same prime factors.

Look at the prime numbers that you found.  There are only three different numbers, even though the 2 repeats.  Those numbers are 2, 3, and 5.

Loop back.  You are asked for the number of distinct prime factors, so the answer must be 3.