6th Grade Math Textbook, Fundamentals

48

• composite numbers; factor again.

••• composite number; factor again.

•••• all prime numbers

48  24 • 3 exponential form

2

222

222

12

6

3

4

108 Chapter 5

5-1

The tree is complete when the factors are all prime numbers.

The prime factorization of 48 is 2 • 2 • 2 • 2 • 3, or 2^4 • 3.

If you had chosen 3 and 16 as the first pair of factors for 48,

the prime factorization would remain 2^4 • 3.

Another way to find the prime factorization is to divide by prime

numbers until the quotient is 1.

Find the prime factorization of 24.

The prime factorization of 24 is 2 • 2 • 2 • 3 or 2^3 • 3.

A number is divisibleby another number if there is no remainder

when you divide. You can use the divisibility rules to help you find

the prime factorization of greater whole numbers.

prime factorization

1 1

or 24

8

4

2

3

2

2

2

2

2

2

3

24

12

6

3

Prime Factorization

Objective To find the prime factorization of a number

A is a whole number greater than 1 that has
exactly twofactors, itself and 1. A is a whole
number greater than 1 that has more than twofactors. The
number 1, which has only one factor, is neither prime nor
composite.

is a way of showing a composite number as the
product of prime numbers. Except for the order of the factors, every
composite number has a unique prime factorization.

To find the prime factorization of a number, you can use a.

Find the prime factorization of 48.

Prime factorization

composite number

prime number

factor tree

• Write 48 at the top of the tree.


• Choose any two whole number
  factors of 48.


• If any factor is notprime, rewrite it
  as a product of two factors.


• Write the prime factors that repeat
  in exponential form. List bases in
  least to greatest order.

Remember:

are numbers that are

multiplied to find a product.

You can factora number or

an expression by writing it as

a product of its factors.

Factors