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
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
