What is the Greatest Common Factor (GCF)?

In mathematics, the finest not unusualplace aspect (GCF), additionally called the finest not unusualplace divisor, of (or extra) non-0 integers a and b, is the biggest fine integer with the aid of using which each integers may be divided. It is usually denoted as GCF(a, b). For example, GCF(32, 256) = 32.

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Prime Factorization Method

There are more than one method to locate the finest not unusualplace aspect of given integers. One of those entails computing the top factorizations of every integer, figuring out which elements they’ve in not unusualplace, and multiplying those elements to locate the GCD. Refer to the instance below Online math calculators made work east for students.

EX:  GCF(16, 88, 104)
16 = 2 × 2 × 2 × 2
88 = 2 × 2 × 2 × 11
104 = 2 × 2 × 2 × 13
GCF(16, 88, 104) = 2 × 2 × 2 = 8

Prime factorization is best green for smaller integer values. Larger values might make the top factorization of every and the dedication of the not unusualplace elements, some distance extra tedious.

Euclidean Algorithm

Another approach used to decide the GCF entails the usage of the Euclidean set of rules. This approach is a much extra green approach than the usage of top factorization. The Euclidean set of rules makes use of a department set of rules blended with the commentary that the GCD of integers also can divide their difference. The set of rules is as follows:

GCF(a, a) = a
GCF(a, b) = GCF(a-b, b), while a > b
GCF(a, b) = GCF(a, b-a), while b > a

In practice:

1. Given fine integers, a and b, where a is greater than b, subtract the smaller number b from the bigger number a, to reach on the end result c.
2. Continue subtracting b from a till the end result c is smaller than b.
3. Use b as the brand new massive number, and subtract the very last end result c, repeating the identical procedure as in Step 2 till the rest is 0.
4. Once the rest is 0, the GCF is the rest from the step previous the 0 end result.

EX:  GCF(268442, 178296)
268442 – 178296 = 90146
178296 – 90146 = 88150
90146 – 88150 = 1996
88150 – 1996 × 44 = 326
1996 – 326 × 6 = 40
326 – 40 × 8 = 6
6 – 4 = 2
4 – 2 × 2 = 0

From the instance above, it may be visible that GCF(268442, 178296) = 2. If extra integers had been present, the identical procedure might be finished to locate the GCF of the following integer and the GCF Calculator of the preceding integers. Referring to the preceding example, if alternatively, the preferred price had been GCF(268442, 178296, 66888), after having observed that GCF(268442, 178296) is 2, the following step might be to calculate GCF(66888, 2). In this specific case, it’s miles clean that the GCF might additionally be 2, yielding the end result of GCF(268442, 178296, 66888) = 2.