# Common Factors Worksheets

What Are Common Factors? "Factors" are numbers we can multiply together to get another number. When we find the factors of two or more numbers, and then find some factors are the same ("common"), then they are the "common factors." A common factor is a number that can be divided into two different numbers, without leaving a remainder. Often numbers can share more than one common factor. It is possible to find the common factors of more than two numbers. Example: 12 and 16. The factors of 12 are: 1, 2, 3, 4, 6 and 12. The factors of 16 are: 1, 2, 4, 8 and 16. So, the common factors of 12 and 16 are: 1, 2 and 4.

• ### Basic Lesson

Demonstrates how to find the least common multiple and greatest common factor of number sets. Also includes practice problems. Find the least common multiple of 3 and 9. List the prime factors of each. 3: 3. 9: 3 × 3. Multiply each factor the greatest number of times it occurs in any of the numbers. 9 has two 3s, so we multiply 3 two times. This gives us 9, the smallest number that can be divided evenly by 3, 9.

• ### Intermediate Lesson

Uses a larger more difficult number sets than the basic lesson. Find the least common multiple of 12 and 80. List the prime factors of each. 12: 2 × 2 × 3. 80: 2 × 2 × 2 × 2 × 5 = 80. Multiply each factor the greatest number of times it occurs in either number. 12 has one 3, and 80 has four 2's and one 5, so we multiply 2 four times, 3 once, and five once. This gives us 240, the smallest number that can be divided by both 12 and 80. Verify: 240 can be divided by both 12 and 80.

• ### Independent Practice 1

10 problems ask for the greatest common factor. 10 problems ask for the least common multiple. Find the greatest common factor for the following pairs of numbers.

• ### Independent Practice 2

20 practice problems that review common factor skills. The answers can be found below.

• ### Homework Worksheet

12 problems to reinforce the lessons and practice pages. An example is provided.

• ### Skill Quiz

10 problems that test common factor skills.

• ### Homework and Quiz Answer Key

Answers for the homework and quiz.

• ### Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

#### Isaac Asimov

"...because any number can be divided by itself and by one, the Greeks (who loved to play games with factors) usually disregarded those two numbers as factors. There is no interesting pattern, after all, in something that hits all numbers without distinction."