Common factors of two or more integers are those which can be divided perfectly without a residue. Factors are integers that can divide another integer perfectly, producing 0. Whenever you examine the factors of two integers, you see that some of them will be the same or have a similar factor. These are referred to as common factors. A factor of a number is an exact multiple of the provided number, or when a number is split precisely by a divisor, the divisor is known as a factor of that number.

A number’s factors cannot be larger than the provided number; they must be less than or equal to the supplied number. Every number has 1 as a common component, and every number is a factor of itself. When we determine the factors of two integers, you observe that certain factors are frequent. This is attributable to the fact that a number may be precisely subdivided by numerous divisors if the number is a multiple of that division.

Factors of 35, for illustration, are 1,5,7,35, and factors of 45 are 1,3,5,9,15, and 45. 1 and 5 are the integers that divide all integers precisely. As a result, the common factors of 35 and 45 are 1 and 5, respectively. The concept of common factors in mathematics states that “when two or more integers are precisely reduced by the same number(s), the common divisors are known as the common factors of the supplied numbers.”

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## How To Find Common Factors?

This is a topic which speaks about the factors that are the numbers or the exact divisors of any particular number. Now look at the steps that will help you find the common factors:

**Step 1:** Jot down all the factors of any given number in a series of separated rows.

**Step 2:** Next you need to keep a check on the various factors that are in common to the set of numbers and then note down the common factors which separate the entire row.

Take for instance, try to find the common factors for the given set of numbers- 8, 12, 20, and 28.

First step: Pen down all the factors for the given set of numbers

Factors of 8- 1, 2, 4, 8

Factors of 12- 1, 2, 3, 4, 6, 12

Factors of 20- 1, 2, 4, 5, 10, 20

Factors of 28- 1, 2, 4, 7, 14, 28

Second step: Common factors here of {8, 12, 20, 28} = 1,2 and 4.

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## Greatest Common Factor

The biggest consistent element of two integers is the GCF- Greatest Common Factor. After all of the components of two or more numbers have been extracted or codified, you may identify the few factors that are shared by the supplied numbers. The biggest common factor is the largest number found among the common factors. Assume p and q are natural numbers. The greatest common factor (GCF) of two natural numbers p and q is the biggest integer that divides p and q. The highest common factor is sometimes referred to as the HCF (Highest Common Factor) or the largest common divisor.

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## Conclusion

The above article talks about the very major component of mathematics that is the base for every student since the beginning. The greatest common factor plays a vital role in the factorization portion. Cuemath, an online platform has proved to be a very effective platform for both students and teachers as it contains all the details that allows both of them to understand the concept in depth.

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