What is the definition for the Greatest Common Factor?

Answer 1

The greatest common factor means the number that is the largest factor between two numbers. For example the greatest common factor of 4 and 6 is 2. 4 has factors of 1,2, and 4. 6 has factors of 1,2,3, and 6. You simply compare the factors of the two numbers and see what the highest number is that they both have.
If you mean Greatest Common Factor (GCF):

The GCF of 2 or more numbers is the greatest number that is a factor of the numbers. For example, the GCF of 18 and 12 would be 6, because that is the largest factor of 18 and 12.
The greatest common factor, or GCF, is the largest integer that divides evenly into two or more given numbers with no remainder.

Answer 2

The greatest common factor(or the greatest common divisor): For two nonzero integers a and b, any integer that is a divisor of both a and b is a common divisor. The greatest of all the common divisors is the greatest common divisor denoted by gcd(a, b) or (a, b), which has the property of being divisible by every other common divisors of a and b.

For example, the gcd(12, 8) is 4.

the positive factors (or divisors) of 12 are 1, 2, 3, 4, 6, and 12.

the positive factors (or divisors) of 8 are 1, 2, 4, and 8.

1, 2, and 4 are all the common divisors of 12 and 8.

Since 4 is the greatest of all the common divisors, it is the greatest common divisor (or the GCF) of 12 and 8, and 4 is also divisible by 1 and 2.

Answer 3

The greatest common factor of two numbers is the largest number that they are both divisible by. If you look at the example of the numbers 22 and 33. The largest number that they are both divisible by is 11 so that is the greatest common factor.

Answer 4

The greatest common factor, or GCF, is the largest positive integer that will divide evenly with no remainder into all the members of a given set of numbers.