# What is the greatest common factor of 21 and 42%3

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## What is the GCF of 21 and 42?

The first step to find the gcf of 21 and 42 is to list the factors of each number. The factors of 21 are 1, 3, 7 and 21. The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42. So, the Greatest Common Factor for these numbers is 21 because it divides all them without a remainder. Read more about Common Factors below.

## How to find the Greatest Common Factor

### GCF example:

The first step is to find all divisors of each number. For instance, let us find the gcf(21, 42).

In this case we have:

• The factors of 21 (all the whole numbers that can divide the number without a remainder) are 1, 3, 7 and 21;
• The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.

The second step is to analyze which are the common divisors. It is not difficult to see that the 'Greatest Common Factor' or 'Divisor' for 21 and 42 is 21. The GCF is the largest common positive integer that divides all the numbers (21, 42) without a remainder.

In the name greatest common divisor, the adjective "greatest" may be replaced by "highest", and the word "divisor" may be replaced by "factor", so that other names include highest common factor (hcf), greatest common measure, among others.

So, the GCF is also known as:

• Greatest common divisor (gcd);
• Highest common factor (hcf);
• Greatest common measure (gcm), or
• Highest common divisor

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