# Common Factor Definition

When a number is divided, it can form two or more factors. But if we divide two numbers separately, their factors can be the same or different. All same factors of two or more numbers are called common factors.

Note:

For example, 7 and 21 have two common factors that are 1 and 7. It is because when these numbers are divided, 1 and 7 come as the answer in both division processes.

## What is the significance of a common factor?

In Mathematics, common factors help the student in solving different problems. Through common factors, you can find the LCM and HCF of the given numbers

Note:

• LCM can be found by multiplying the common factors with the uncommon factors of the given numbers. For example, 2 and 3 have 6 as their LCM when their Prime Factors are multiplied.
• HCF is the multiplication of all common factors of the given numbers. For example, 15 and 35 have 5 as their HCF because it is the only common factor in their dividing factors tree.

Note:

### How to find common factors of two numbers?

It is simple to find common factors of two or more numbers by dividing them simply with prime numbers. You only have to learn the Prime Factorization to find common factors.

Note:

You can read about Prime Factorization here.

It is a process to divide a number with prime factors like 2, 3, 5, 7, etc. When you have divided the given numbers with prime factors, the same factors can be written in a set that is termed a Set of Common Factors.

Example 1:

Find common factors of 5, 10, and 25.

Solution:

To find a common factor of these numbers, we need to divide them by prime numbers.

5 = 1 x 5
10 = 1 x 2 x 5
25 = 1 x 5 x 5

As we can see, “5” appears in the factors of all the given numbers, which means that “5” is the common factor of these numbers.

### What is the difference between a common factor and a common multiple?

Many students consider a common factor and common multiple same. But these are not same. Common factors consist of those dividers of the given numbers that are the same for all those numbers. On the other hand, common multiples are those numbers that come in sequence while we are counting the number in a multiplication.

Note:

You can read about Common Multiples here.

### FAQ's

Do 3 and 5 have common factors?

Yes, “1” is the common factor for 3 and 5.

What is the common factor of all natural numbers?

The common factor of all natural numbers is “1” because it divides all numbers from this set.

Can we find HCF through common factors?

Yes, HCF is the multiplication of all the common factors of the given numbers.

Is common multiple and common factor same?

No, the common multiple and common factor is not same.

What is the smallest common factor of two natural numbers?

The smallest common factor of two natural numbers is “1”.

Can “0” be a common factor?

No, “0” can’t be a factor because it can neither divide nor multiply any number.