greatest common factor(gcf)
the greatest of the common factors of two or more numbers
The Greatest Common Factor (GCF) is the largest number that divides two or more integers evenly, without leaving a remainder.
To find the GCF of two numbers, we can use the method of prime factorization. We first factor each number into its prime factors, and then identify the common prime factors, taking the lowest exponent of each common prime factor. Finally, we multiply the common prime factors together to get the GCF.
For example, let’s find the GCF of 36 and 48.
First, we factor each number into its prime factors:
– 36 = 2^2 * 3^2
– 48 = 2^4 * 3^1
Next, we identify the common prime factors, taking the lowest exponent of each:
– The common prime factors are 2 and 3.
– The lowest exponent of 2 is 2, which occurs in both numbers.
– The lowest exponent of 3 is 1, which occurs in one of the numbers.
Finally, we multiply the common prime factors together to get the GCF:
GCF(36, 48) = 2^2 * 3^1 = 12
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