What is the greatest common factor of 12 and 34?

Greatest Common Factor Calculator / Converter

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What is the GCF of 12 and 34?

The first step to find the gcf of 12 and 34 is to list the factors of each number. The factors of 12 are 1, 2, 3, 4, 6 and 12. The factors of 34 are 1, 2, 17 and 34. So, the Greatest Common Factor for these numbers is 2 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(12, 34).

In this case we have:

The factors of 12 (all the whole numbers that can divide the number without a remainder) are 1, 2, 3, 4, 6 and 12;
The factors of 34 are 1, 2, 17 and 34.

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 12 and 34 is 2. The GCF is the largest common positive integer that divides all the numbers (12, 34) 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 65 and 68

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Martina Birk

Update: 2023-03-28

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