**Factors and Multiples**

Factors and Multiples

Prime Numbers

Factors and Prime Factors

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12 X 12 = 12

= 144

Square and Square Root

Cube and Cube Root

A prime number is a natural number

greater than 1 that has no positive divisors other than 1 and itself.

Example: 2, 3, 5, 7, 11, 13, 17 etc

Composite Numbers

Numbers that can be written as a product of two or more prime numbers.

Example 4, 6, 8, 9, 10, 12, 14, 15 etc

Factors and Multiples

Factors

2 X 3 = 6

1 X 6 = 6

2 and 3 are factors of 6

Multiples

2, 4, 6, 8, 10 etc are multiples of 2

3, 6, 9, 12, 15 etc are multiples of 3

Note that 6 is the lowest common multiple between 2 and 3.

List all the factors of 12

1 X 12 = 12

2 X 6 = 12

3 X 4 = 12

1, 2, 3, 12, 6, 4 are factors of 12. There are 6 factors out of which 2 and 3 are prime factors.

Prime factorization of 12

12 = 2 X 2 X 3

= 2 X 3

2

A composite number can be written as a product of its prime factors. We call this prime factorization.

12

2

6

2

3

3

1

List the factors of 96

Prime Factorization of 96

96

2

48

2

24

2

12

2

6

2

3

3

1

1, 3, 6, 12, 24, 48, 96,

2, 4, 8,

16, 32.

96 = 2 X 2 X 2 X 2 X 2 X 3

= 2 X 3

5

144

= 12

2

12 X 12 X 12 = 12

3

1728

= 12

= 1728

2 X 3 X 2 X 3 X 2 X 3

= (2 X 3) X (2 X 3) X (2 X 3)

= (2 X 3)

3

2 X 2 X 2 X 3 X 3 X 3

= 2 X 3

=(2 X 3)

3

3

3

484

Find

by prime factorization

484

242

121

11

1

11

11

2

2

484

= 2 X 2 X 11 X 11

= 2 X 11

2

2

= (2 X 11)

2

484

= 2 X 11

= 22 (Answer)

= ((2 X 11)

2

Find the cube root of 1000 by prime factorization

1000

500

250

125

5

2

2

2

5

25

5

5

1

= 2 X 2 X 2 X 5 X 5 X 5

= 2 X 5

3

3

= (2 X 5)

3

1000

1000

=

(2 X 5)

3

= 2 x 5

= 10 (Answer)

1000

=

(2 X 5)

3

=

(2 X 5)

3

[

]

1

3

= 2 X 5

Note

3

X

1

3

Lowest Common Multiple

Greatest Common Factor

**225, 750**

**75, 250**

**15, 50**

**3, 10**

**5**

**5**

**3**

**225, 750**

**75, 250**

**15, 50**

**3, 10**

**3**

**5**

**5**

**3**

**2**

**1, 10**

**1, 5**

**5**

The GCF = 3 x 5 x 5

= 75

The LCM = 3 x 5 x 5 x 3 x 2 x 5

= 3 x 5 x 2

= 2, 250

2

3

**1, 1**