# What is the greatest common factor of 10, 12 and 14?

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## What is the GCF of 10, 12 and 14?

The first step to find the gcf of 10, 12 and 14 is to list the factors of each number. The factors of 10 are 1, 2, 5 and 10. The factors of 12 are 1, 2, 3, 4, 6 and 12. The factors of 14 are 1, 2, 7 and 14. So, the **Greatest Common Factor** for these numbers is 2 because it divides all them without a remainder. Read more about Common Factors below.

To use the GCD / GCF / HCF Calculator below just enter a set of numbers separated by commas (,).

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## 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(10,12,14).

In this case we have:

- The factors of 10 (all the whole numbers that can divide the number without a remainder) are 1, 2, 5 and 10;
- The factors of 12 are 1, 2, 3, 4, 6 and 12;
- The factors of 14 are 1, 2, 7 and 14.

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 10, 12 and 14 is 2. The GCF is the largest common positive integer that divides all the numbers (10,12,14) without a remainder.

The GCF is also known as:

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

To learn more about GCF/GCD, watch this video from Khan Academy or/and read this arcticle.

### Greatest Common Factor Calculator

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