What is the greatest common factor of 54 and 105?

Greatest Common Factor Calculator / Converter

You have reached us maybe looking for answers to the questions like: What is the greatest common factor of 54 and 105? or what is the highest common factor (HCF) of 54 and 105?

What is the GCF of 54 and 105?

The first step to find the gcf of 54 and 105 is to list the factors of each number. The factors of 54 are 1, 2, 3, 6, 9, 18, 27 and 54. The factors of 105 are 1, 3, 5, 7, 15, 21, 35 and 105. So, the Greatest Common Factor for these numbers is 3 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(54, 105).

In this case we have:

The factors of 54 (all the whole numbers that can divide the number without a remainder) are 1, 2, 3, 6, 9, 18, 27 and 54;
The factors of 105 are 1, 3, 5, 7, 15, 21, 35 and 105.

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 54 and 105 is 3. The GCF is the largest common positive integer that divides all the numbers (54, 105) 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

Greatest Common Factor Calculator

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GCF Examples

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GCF of 11,12 and 14
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GCF of 1,5 and 10

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Lourie Helzer

Update: 2023-03-28

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