Common Factors

Nov 30, 2022, 16:45 IST

A factor of a number is the exact divisor of the number. Every factor of the number is equal to or less than the number; that is, it cannot be greater than the number. Every number has at least two factors, and some have more than the two. For example, 1, 2, 4, and 8 are factors of 8. Thus,1 is a factor of every number, and the every number is a factor of its own. It can be said that a given number of factors is finite. Also, check the highest common factor of any number here.

Definition

In Mathematics, common factors are the factors which are common to two and more numbers. In simple words, a common factor is the number which is a set of two or more numbers that will be divided exactly.

Common Factors of Two Numbers

To find the common factors of the two given numbers, first, list all the factors of the two given numbers separately and then compare the numbers. Thus, write the factors which are common to both the given numbers. These factors are known as common factors of the given two numbers.

How to Find the Common Factors

As mentioned above, the factors is a number that divides the given number completely. But how to check if two or more numbers have the common factors between them.

Below are the following steps to find the common factors-

• Write the factors of the given numbers.
• Find the common factor present in them.

More Helpful Link About- Liters to Milliliters, Ratio to Percentage

Solved Examples

Q1. Determine the common factors of 18 and 24.

Ans. 1 x 18 =18

2 x 9 = 18

3 x 6 = 18

6 x 3 = 19

9 x 2 = 18

Factor of 18 is 1, 2, 3, 6, 9 and 18

1 x 24 = 24

2 x 12 = 24

3 x 8 = 24

4 x 6 = 24

6 x 4 = 24

8 x 3 = 24

12 x 2 = 24

Factor of 24 is 1, 2, 3, 4, 6, 8 and 12

The common factors of 18 and 24 = 1, 2, 3, and 6.

Q2. Find the common factors of 25, 40, and 27?

Ans. 1 x 25 = 25

5 x 5 = 25

Factor of 25 = 1, 5 and 25

1 x 40 = 40

2 x 20 = 40

4 x 10 = 40

5 x 8 = 40

8 x 5 = 40

10 x 4 = 40

Factor of 40 = 1, 2, 4, 5, 8, 10 and 40

1 x 27 = 27

3 x 9 = 27

9 x 3 = 27

Factor of 27 = 1, 3, 9 and 27

Therefore, the common factor of 25, 40, and 27 is 1

Frequently Asked Question (FAQs)

Q1. How do you identify common factors?

Ans. To identify the common factors of the two given numbers, first, list all the factors separately and then compare the given numbers. Thus, write the factors which are common to both numbers. These factors are called common factors of given two numbers.

Q2. What is the common factor rule?

Ans. In mathematics, the common factors state that "when the two or more numbers are simply divided by the same number, then those common divisors are known as common factors of the given numbers.

Q3. What is the greatest common factor in math?

Ans. The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.

Q4. What if there are no common factors?

Ans. Two or more numbers with no common positive integer factor other than are called "coprime." Any two or more prime numbers are necessarily coprime. For example, 5, 11, 37. Two or more composite numbers can also be coprime, providing their sets of prime factors are disjoint.

Q5. What is the lowest common factor?

Ans. The lowest common multiple (LCM) is the lowest multiple shared by the two or more numbers.