# SAT Math: Arithmetic

## Factors

How many factors do the numbers 18 and 20 have in common?

A.   0

B.   1

C.   2

D.   3

E.   4

## Knowsys Method

Read the question carefully.  You are looking for factors (not multiples).  You also want to use a different method for finding the factors of a number than the method that you would use for finding the prime factors of a number.

Identify the bottom line.  Factors in both 18 and 20.

Assess your options.  You do not want to use a factor tree for this problem!  Factor trees are for finding the prime factors of an integer.  You need to find all of the positive integers that divide evenly into these numbers.  In order to do that, you will use a factor rainbow.  List the factors in pairs, starting with 1 times the number.  That is your outer edge of the rainbow.  Then move inwards, asking yourself "Does 2 work?  Does 3?"  When there are no more factors between the inside edges of your rainbow that work, then you are finished.  This is a systematic approach that ensures that you do not miss any factors.

Attack the problem.

Start by creating a factor rainbow for each number:

Then compare your two rainbows.  Which factors are in both rainbows?   In this case, only the 1 and the 2 are in both rainbows.  It will not always be the case that only the first numbers are the same, so you must create the whole rainbow each time to be sure of your answer.

Loop back.  You found only 2 numbers in common between 18 and 20.  That matches your bottom line, so select the correct answer.

The correct answer is (C).

This is a medium level question.

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.

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