Greatest Common Factor Least Common Multiple Factorization Greatest Common Factor Least Common Multiple

Why Factor? Factors allow you to break composite numbers down to their component parts. Factors are used to simplify fractions. Factors are used to identify the greatest common factor (GCF) and the least common multiple (LCM). A number can be written as the product of its prime factors.

Find Factor Pairs for 24 Start with 1: 1 x 24 = 24 2: 2 x 12 = 24 The commutative property shows the same pairs: 1 x 24 = 24 x 1 2 x 12 = 12 x 2 3 x 8 = 8 x 3 4 x 6 = 6 x 4

Prime Factorization Prime numbers are numbers that have only one and the number as factors. “1” is neither prime or composite. Composite numbers can be written as products of their prime factors.

Factorization Upside Down Division

Prime factorization of 24 2 24 2 12 2 6 3 Prime Factorization is 2 x 2 x 2 x 3

Prime factorization of 28 2 28 2 14 7 Prime Factorization is 2 x 2 x 7

Prime factorization of 15 3 15 5 Prime Factorization is 3 x 5

Prime factor 40 2 40 2 20 2 10 5 Prime Factorization is 2 x 2 x 2 x 5

Greatest Common Factor (GCF) Definition: The largest factor that divides evenly into 2 or more numbers. Examples: 3 and 7 have no common factors other than 1 4 and 6 have the greatest common factor of 2 6 and 24 have a greatest common factor of 6 10 and 15 have a GCF of 5

Greatest Common Factor Use Factorization

Prime factor 28 and 16 to find the GCF 2 28 2 14 7 Prime Factorization of 28: 2 x 2 x 7 2 16 2 8 2 4 2 Prime Factorization of 16: 2 x 2 x 2 x 2

Prime factor 28 and 16 2 28 2 14 7 Prime Factorization of 28: 2 x 2 x 7 2 16 2 8 2 4 2 Prime Factorization of 16: 2 x 2 x 2 x 2 GCF is 2 x 2 = 4

Factor both numbers 28 and 16 at the same time 2 28 16 2 14 8 7 4 The GCF is the product of the common prime factors: 2 x 2 = 4

Factor both numbers: 24 and 30 2 24 30 3 12 15 4 5 The GCF is the product of the common prime factors: 2 x 3 = 6

Factor both numbers: 28 and 42 G 2 28 42 14 21 2 3 The GCF is the product of the common prime factors: 2 x 7 = 14

Factor both numbers: 12 and 30 G 2 12 30 3 6 15 2 5 The GCF is the product of the common prime factors: 2 x 3 = 6

Least Common Multiple Use Factorization

Factor both numbers 28 and 16 at the same time 2 28 16 2 14 8 7 4 The LCM is the product of ALL the factors: 2 x 2 x 7 x 4 = 112

Factor both numbers: 24 and 30 2 24 30 3 12 15 4 5 The LCM is the product of ALL of the factors: 2 x 3 x 4 x 5 = 120

Factor both numbers: 28 and 42 2 28 42 14 21 2 3 The LCM is the product of ALL of the factors: 2 x 7 x 2 x 3 = 84

Factor both numbers: 12 and 30 2 12 30 3 6 15 2 5 The LCM is the product of ALL of the factors: 2 x 3 x 2 x 5 = 60

Greatest Common Factor and Least Common Multiple

Factor both numbers: 10 and 30 G 5 10 30 2 2 6 1 3 GCF: 5 x 2 = 10 LCM: 5 x 2 x 1 x 3 = 30

Factor both numbers: 12 and 40 G 2 12 40 2 6 20 3 10 GCF: 2 x 2 = 4 LCM: 2 x 2 x 3 x 10 = 120

Factor both numbers: 12 and 40 G 2 12 40 2 6 20 3 10 GCF: 2 x 2 = 4 LCM: 2 x 2 x 3 x 10 = 120

Simplifying Fractions Greatest Common Factor

Simplify 24/30 2 24 30 3 12 15 4 5 The fraction 24/30 2 24 30 3 12 15 4 5 The fraction 24/30 simplifies to 4/5 (The GCF was used: 24/6 = 4, 30/6 = 5)

Simplify 28/42 2 28 42 7 14 21 2 3 The fraction 28/42 2 28 42 7 14 21 2 3 The fraction 28/42 simplifies to 2/3 (The GCF was used: 28/14 = 2, 42/14 = 3)

Simplify 12/40 2 12 40 2 6 20 3 10 The fraction 12/40 2 12 40 2 6 20 3 10 The fraction 12/40 simplifies to 3/10 (The GCF was used: 12/4 = 3, 40/4 = 10)