Prime Time 1.6

Objective:

Write prime factorization using exponents

Is it divisible by Only if…

2 The ones digit is divisible by 2

3 The sum of the digits is divisible by 3

4 The last two digits of the # are divisible by 4

5 It ends in 0 or 5

6 The # is divisible by 2 and 3

9 The sum of the digits is divisible by 9

10 The # ends in 0

Did you know?

• Did you know that prime means “first or original”?

• Did you know that composite means “made up of different parts”?

• Did you know that factor means “one thing that influences or contributes to another”?

• How do these everyday meanings related to their math meanings?

Tell whether each number is prime, composite, or neither

• 1) 28

• 2) 11

• 3) 1

• 4) 2

Prime Factorization

• Prime Factorization: a composite number expressed as a product of prime numbers.

• Factor Trees are often used to help you organize your prime factorization.

Example

• Find the prime factorizations of the numbers:

54 72

• List the numbers in order from least to greatest

• Can you write the answers in exponent form?

Powers and Exponents

• A product of identical factors can be written using an exponent and a base.

• 32 = 2 x 2 x 2 x 2 x 2 = 2^5Base

Exponent

Numbers expressed using exponents are called powers.

Powers Words

2 ^ 5 2 to the fifth power

3 ^ 2 3 to the second power or 3 squared

10 ^ 3 10 to the third power or 10 cubed

7 ^ 4 7 to the forth power

What about when the exponent is 0 or 1?

• If no exponent is given the exponent is considered to be 1.

• This does not change the value.

• For example:• 5 ^ 1 = 5

• If the exponent is given is 0, the value is one.

• (This is 7th grade math)

• For example:• 5 ^ 0 = 1

Practice

• Write using exponents:

• 5 x 5 x 5 x 5 =

• 6 x 6 x 6 =

• 12 x 12 x 12 x 12 =

Practice

• Find the prime factorization of the following numbers. Write the final answer using exponents.

8 64 256

Calculator

• You can use a calculator to evaluate powers.

• To find 3 to the forth power press

3 ^ 4

What is the answer?