PRIME NUMBERS

 

Prime number is a whole number with exactly two factors: itself and 1.

 

Example:

1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37

 

 

COMPOSITE NUMBERS

 

Composite Number is a whole number with more than 2 factors.

 

Example:

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32

 

Every composite number can be written as the product of prime factors.

Example:  540 = 2 x 2 x 3 x 3 x 3 x 5

 

 

PRIME FACTORIZATION

 

Prime factorization is that writing a number as the product of its prime factors.

 

Example:

Find the prime factor of 540

 

 

540

 

 

 

 

 

2

 

270

 

 

 

 

 

2

 

135

 

 

 

 

 

3

 

45

 

 

 

 

 

3

 

15

 

 

 

 

 

3

 

5

 

 

GREATEST COMMON FACTOR

 

Example:

 

Find the greatest common factor of 75, 90 and 420

 

Write each number as a product of its prime factors:

 

75 = 3 x 5 x 5

90 = 2 x 3 x 3 x 5

420 = 2 x 2 x 3 x 5 x 7

 

Find the common factors, and multiply them.

Greatest Common Factor (GCF):  3 x 5 = 15

 

Second Method:

 

List the factors of 75, 90, 420

:

75:  1,3,5,6,15,25,75

90:  1,2,3,5,6,9,10,15,18,30,45,90

420:  1,2,3,4,5,6,7,10,12,15,20,21,28,30,35,42,60,70,84,105,140,210,420

 

Greatest Common Factor (GCF) = 15

 

 

LOWEST COMMON MULTIPLE (LCM)

 

Example:

 

Find the lowest common multiples of 8, 12 and 30

 

List the multiples of 8, 12 and 30

 

Multiples of 8:  8, 16, 24, 32, 40, 48, 60, 72, 80, 88, 96, 104, 112, 120, 128, 136

Multiples of 12:  12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144

Multiples of 30:  30, 60, 90, 120, 150, 180

 

The lowest common multiple (LCM) = 120

 

Method 2:

 

Write each number as the product of prime factors:

 

8 = 2 x 2 x 2

12 = 2 x 2 x 3

30 = 2 x 3 x 5

 

Take one 2, one 2, one 3, 2 and 5.  Multiply the number each other.

The lowest common multiple (LCM) = 2 x 2 x 2 x 3 x 5 = 120