How To Find The Greatest Common Factor (Gcf) Of Two Or More Numbers: A Guide With Examples.

Greatest Common Factor

The largest factor that two or more numbers have in common.

The greatest common factor (GCF) is the largest number that divides evenly into two or more given numbers. It is also called the greatest common divisor (GCD).

To find the GCF of two or more numbers, you can start by listing all of their factors. Then, identify the common factors and choose the largest one. For example, to find the GCF of 12 and 18:

– The factors of 12 are 1, 2, 3, 4, 6, and 12.
– The factors of 18 are 1, 2, 3, 6, 9, and 18.
– The common factors are 1, 2, 3, and 6.
– The largest common factor is 6, so the GCF of 12 and 18 is 6.

Alternatively, you can use prime factorization to find the GCF. To do this, write each number as a product of primes, and then multiply the common factors with the smallest exponents. For example:

– 12 = 2 x 2 x 3
– 18 = 2 x 3 x 3
– The common prime factors are 2 and 3.
– The exponents for 2 are 2 in 12 and 1 in 18, so we choose 2 to the power of 1, which is 2.
– The exponent for 3 is 1 in both numbers, so we choose 3 to the power of 1, which is 3.
– The product of these factors is 2 x 3, which is 6.

Both of these methods will give you the same answer. Finding the GCF is useful for simplifying fractions and solving problems related to factors and divisibility.

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