Math 020 Factoring Worksheet With Answers - Cuny, 2009 printable pdf download

Math 020 Factoring Worksheet With Answers - Cuny, 2009

MATH 020 – Factoring

Fall 2009

Prime Numbers

the ﬁrst eight prime numbers are: 1, 2, 3, 5, 7, 11, 13, 17

where a prime number is a number that is only divisible by 1 and itself.

When we say “divisible” here, we mean that the result of the division is a whole number only.

for example, the number seven is divisible by 1 and by 7 only:

= 7 and

= 1

try dividing 7 by any other number and the result is NOT a whole number:

and

are not whole numbers

Factors

When a number is expressed as a product of two or more numbers, those numbers are called Factors.

For example

30 = 5

We say that “ 5 and 6 are factors of 30”.

If we further break down the factors until all the factors are prime numbers, we say that we have the

Prime Factors of that number.

30 = 5

6 = 5

The prime factors of 30 are 5, 3 and 2.

Greatest Common Factor or “GCF”

When we compare the factors of two numbers to see what prime factors they have in common, we

say that we have found their “common prime factors”, or, prime factors that they have in common.

The product of these factors is called the Greatest Common Factor, or GCF for short.

Example:

30 = (5)(3)(2)

75 = (5)(5)(3)

The prime numbers 5 and 3 are both factors that are common to 30 and 75. The product of these

factors is 3

5 = 15. Thus, the “Greatest Common Factor” of 30 and 75 is 15. To check this result,

divide 15 into 30 and then into 75, and verify that in each case the result is a whole number.

= 2

and

= 5

In each case, the quotients are whole numbers, which conﬁrms that 15 is the GCF.

Math 020 Factoring Worksheet With Answers - Cuny, 2009