How to Find the Greatest Common Factor (GCF) of Two or More Numbers: Methods and Examples

Greatest common factor

The greatest common factor (GCF) of two or more numbers is the largest positive integer that divides each of the numbers without leaving a remainder

The greatest common factor (GCF) of two or more numbers is the largest positive integer that divides each of the numbers without leaving a remainder. In other words, it is the largest number that is a common factor of all the given numbers.

To find the greatest common factor of numbers, there are a couple of methods you can use:

1. Prime Factorization Method:
– Find the prime factorization of each number. Prime factorization is the process of breaking down a number into its prime factors.
– Identify the common prime factors of all the given numbers.
– Multiply the common prime factors together to obtain the GCF.

Example: Find the GCF of 24 and 36.
– The prime factorization of 24 is 2^3 * 3.
– The prime factorization of 36 is 2^2 * 3^2.
– The common prime factors are 2^2 and 3.
– Multiply the common prime factors together: GCF = 2^2 * 3 = 12.

2. Division Method (also known as the Euclidean algorithm):
– Divide the larger number by the smaller number.
– Take the remainder from the division and divide the smaller number by this remainder.
– Repeat the process of dividing the previous remainder by the new remainder until the remainder becomes zero.
– The last non-zero remainder is the GCF.

Example: Find the GCF of 48 and 72 using the division method.
– Divide 72 by 48, the remainder is 24.
– Divide 48 by 24, the remainder is 0.
– The last non-zero remainder is 24, so the GCF is 24.

Both methods will give you the same GCF. It’s a matter of personal preference which method you choose to use. The GCF is useful in simplifying fractions, finding common denominators, and solving equations involving fractions.

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