prime factorization

Prime Prime FactorizationFactorization

A prime number is a whole number greater than 1 that has exactly two factors, 1 and itself.

Three is a prime number because its only factors are 1 and 3. What are the rest of the prime numbers?

A composite number is a whole number that has more than two factors.

Six is a composite number because it has more than two factors—1, 2, 3, and 6. The number 1 has exactly one factor and is neither prime nor composite.

Tell whether each number is prime or composite.

A. 11

11 is prime.

The factors of 11 are 1 and 11.

B. 16

16 is composite.

The factors of 16 are 1, 2, 4, 8, and 16.

Tell whether each number is prime or composite.

C. 14

14 is composite.

The factors of 14 are 1, 2, 7, and 14.

D. 7

7 is prime.

The factors of 7 are 1 and 7.

A composite number can be written as the product of its prime factors. This is called the prime factorization of the number.

You can use a factor tree to find the prime factors of a composite

number.

You can write prime factorization by using exponents. The exponent tells how many times to use the base as a factor.

Writing Math

Write the prime factorization of each number.

248 · 3

4 · 2

2 · 2

Write 24 as the product oftwo factors.

Continue factoring until allfactors are prime.

The prime factorization of 24 is 2 · 2 · 2 · 3 or 23 · 3.


150

30 · 5

10 · 3

2 · 5

Write 150 as the productof two factors.

Continue factoring until all factors are prime.

The prime factorization of 150 is 2 · 3 · 5 · 5, or 2 · 3 · 52.


36

18 · 2

9 · 2

3 · 3

Write 36 as the product oftwo factors.

Continue factoring until allfactors are prime.

The prime factorization of 36 is 2 · 2 · 3 · 3 or 22 · 32.

Write the prime factorization of the number.

90

45 · 2

9 · 5

3 · 3

Write 90 as the productof two factors.

Continue factoring until all factors are prime.

The prime factorization of 90 is 3 · 3 · 5 · 2, or 2 · 32 · 5.

ASSIGNMENTASSIGNMENT

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You can also use a step diagram to find the prime factorization of a number. At each step, divide by

the smallest possible prime number. Continue dividing until

the quotient is 1.

Repeated DivisionRepeated Division

4040 22

Start by dividing Start by dividing by the smallest by the smallest prime number.prime number.

2020Keep using 2 Keep using 2 until it will not until it will not work anymore.work anymore.

22

101022 55

2 x 2 x 2 x 5 = 2³ x 52 x 2 x 2 x 5 = 2³ x 5

5511

When you get to 1 When you get to 1 you are finishedyou are finished

Let’s try another one…Let’s try another one…

4242 22

Start by dividing Start by dividing by the smallest by the smallest prime number.prime number.

21212 will no longer 2 will no longer work so you work so you need to try the need to try the next prime next prime number…3!number…3!

77

33When you When you get to 1 get to 1 you are you are finishedfinished

2 x 3 x 72 x 3 x 7

77

11

Now you try!Now you try!

181822

9933

3333

117722

7714142828

11

22

2 x 32 x 322 2222 x 7 x 7


325

32565131

5513

Divide 325 by 5. Write the quotientbelow 325.

Stop when the quotient is 1.

The prime factorization of 325 is 5 · 5 · 13, or52 · 13.


275

27555111

5511

Divide 275 by 5. Write the quotientbelow 275.


The prime factorization of 275 is 5 · 5 · 11, or52 · 11.


476

476238119

171

22

717

Divide 476 by 2. Write the quotient below 476.

Keep dividing by a prime number.


The prime factorization of 476 is 2 · 2 · 7 · 17, or22 · 7 · 17.

There is only one prime factorization for any given composite number. The last example began by dividing 476 by 2, the smallest prime factor of 476. Beginning with any prime factor of 476 gives the same result.

476238119

171

22

717

4766834

171

72

217

The prime factorizations are 2 · 2 · 7 · 17 and7 · 2 · 2 · 17, which are the same as 17 · 2 · 2 · 7.

prime factorization

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