Use the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum
of two whole numbers with no common factor. Find the greatest common factor (GCF) and least common multiple (LCM) of two or more whole numbers.

Use factors and multiples to determine prime factorization.

Arkansas Academic Standards:
6.NS.B.4

Find the greatest common factor of two whole numbers less than or equal to 100 using prime factorization as well as other methods

Find the least common multiple of two whole numbers less than or equal to 12 using prime factorization as well as other methods

Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor
For example, express 36 + 8 as 4 (9 + 2).

Arizona - K-12 Academic Standards:
6.NS.B.4

Use previous understanding of factors to find the greatest common factor and the least common multiple.

Find the greatest common factor of two whole numbers less than or equal to 100.

Find the least common multiple of two whole numbers less than or equal to 12.

Use the distributive property to express a sum of two whole numbers 1 to 100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9+2).

Common Core State Standards:
Math.6.NS.4 or 6.NS.B.4

Find the greatest common factor of two whole numbers less than or
equal to 100 and the least common multiple of two whole numbers
less than or equal to 12. Use the distributive property to express a
sum of two whole numbers 1–100 with a common factor as a multiple
of a sum of two whole numbers with no common factor. For example,
express 36 + 8 as 4 (9 + 2).

Georgia Standards of Excellence (GSE):
6.PAR.6.2

Determine greatest common factors and least common multiples using a variety of strategies to make sense of applicable problems.

Massachusetts Curriculum Frameworks:
6.NS.B.4

Use prime factorization to find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two relatively prime numbers. For example, express 36 + 8 as 4(9 + 2)

North Carolina - Standard Course of Study:
6.NS.4

Understand and use prime factorization and the relationships between factors to:

Find the unique prime factorization for a whole number.

Find the greatest common factor of two whole numbers less than or equal to 100.

Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or
equal to 100.

Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators.

New York State Next Generation Learning Standards:
6.NS.4

Find the greatest common factor of two whole numbers less than or equal to 100. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor other than 1. e.g., Express 36 + 8 as 4(9 + 2). Find the least common multiple of two whole numbers less than or equal to 12.

Tennessee Academic Standards:
6.NS.B.4

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

Pennsylvania Core Standards:
CC.2.1.6.E.3

Develop and/or apply number theory concepts to find common factors and multiples.

Pennsylvania Core Standards:
M06.A-N.2.2.1

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.

Pennsylvania Core Standards:
M06.A-N.2.2.2

Apply the distributive property to express a sum of two whole numbers, 1 through 100, with a common factor as a multiple of a sum of two whole numbers with no common factor.

Florida - Benchmarks for Excellent Student Thinking:
MA.6.NSO.3.1

Given a mathematical or real-world context, find the greatest common factor and least common multiple of two whole numbers.

Florida - Benchmarks for Excellent Student Thinking:
MA.6.NSO.3.2

Rewrite the sum of two composite whole numbers having a common factor, as a common factor multiplied by the sum of two whole numbers.

Florida - Benchmarks for Excellent Student Thinking:
MA.6.NSO.3.4

Express composite whole numbers as a product of prime factors with natural number exponents.

6th Grade Math - Factors & Multiples Lesson

Factors are numbers that equal a given number when multiplied together.
The factors of 20 are 1, 2, 4, 5, 10, and 20 because:

1 × 20

=

20

2 × 10

=

20

4 × 5

=

20

The greatest common factor is the greatest factor that two or more numbers have in common.

Example:

First, find the factors of 56 and 84.

56:

1, 2, 4, 7, 8, 14, 28, 56

84:

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

The common factors of 56 and 84 are 1, 2, 4, 7, 14, and 28.

So, the greatest common factor of 56 and 84 is 28.

A multiple of a number is the product of the number and an integer. The first 5 multiples of 9 are 9, 18, 27, 36, and 45 because:

9 × 1

=

9

9 × 2

=

18

9 × 3

=

27

9 × 4

=

36

9 × 5

=

45

The least common multiple is the least multiple that two or more numbers have in common.

Example:

Start by listing multiples of 8 and 6.

8:

8, 16, 24, 32, 40

6:

6, 12, 18, 24, 30

The lowest number 8 and 6 both have as a multiple is 24.

So, 24 is the least common multiple of 8 and 6.

The distributive property can be used to write the sum of two numbers as the product of a common factor and a sum.

Example:

First, find the greatest common factor of 18 and 21.

The factors of 18 and 21 are listed below.

18:

1, 2, 3, 6, 9, 18

21:

1, 3, 7, 21

So, the greatest common factor of 18 and 21 is 3.

Write both numbers in the expression as a multiple of 3.

18 + 21 = 3 × 6 + 3 × 7

Then, use the distributive property to write the expression as a product of 3 and the sum of 6 and 7.