Prime Factorization

Vocabulary

100

The result of two or more whole numbers when multiplied together.

OR

The answer to a multiplication problem.

Product

200

One of two (or more) numbers multiplied together to get a product.

Factor

300

A whole number with only two factors: 1 and itself.

Prime Number

400

A whole number with more than two factors.

Composite Number

500

The longest string of multiplication for a number, using ONLY prime numbers.

Prime Factorization

600

In an exponential expression, this part tells us which number is being multiplied.

(Hint: the "3" in 3²)

Base

700

In an exponential expression, this tells us how many times a number is being multiplied.

(Hint: the "2" in 3²)

Exponent

Prime Factorization

100

10

5 x 2

200

12

2 x 2 x 3

or 

2² x 3

300

16

2 x 2 x 2 x 2

or

2⁴

400

20

2 x 2 x 5

or

2² x 5

500

36

2 x 2 x 3 x 3

or

2² x 3²

600

42

2 x 3 x 7

700

96

2 x 2 x 2 x 2 x 2 x 3

or

2⁵ x 3

Prime Factorization (Challenging)

100

120

2 x 2 x 2 x 3 x 5

or

2³ x 3 x 5

200

100

2 x 2 x 5 x 5

or 

2² x 5²

300

150

2 x 3 x 5 x 5

or

2 x 3 x 5²

400

210

2 x 3 x 5 x 7

500

360

2 x 2 x 2 x 3 x 3 x 5

or

2³ x 3² x 5

600

450

2 x 3 x 3 x 5 x 5

or

2 x 3² x 5²

700

960

2 x 2 x 2 x 2 x 2 x 2 x 3 x 5

or

2⁶ x 3 x 5

Simplifying Prime Factorization

100

2 x 2

2²

200

3 x 3 x 3

3³

300

2 x 2 x 3

2³ x 3

400

2 x 2 x 2 x 3 x 3

2³ x 3²

500

2 x 2 x 3 x 5

2² x 3 x 5

600

2 x 2 x 3 x 5 x 5

2² x 3 x 5²

700

2 x 3 x 3 x 5 x 5 x 5 x 7

2 x 3² x 5³ x 7

Prime Factorization to Composite

100

2 x 2 x 2

8

200

2 x 3 x 3

18

300

2 x 5 x 5

50

400

2 x 2 x 2 x 2 x 2

32

500

2 x 2 x 3 x 3

36

600

2 x 2 x 5 x 7 

140

700

2 x 3 x 5 x 7

210

Prime Factorization to Composite (w/ Exponents)

100

2² x 3

12

200

3²

9

300

2³ x 3

24

400

2 x 5²

50

500

2³ x 3² x 5

360

600

2⁴ x 5

80

700

2² x 3² x 5²

900