The greatest usual factor (GCF) of two or more numbers is the largest variable they share. The greatest typical factor might be found using a variety of methods such together listing factors, making use of prime factorization, or Euclid"s algorithm, among others. The GCF of two numbers, such as 12 and also 16, deserve to be denoted as GCF(12, 16).

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For smaller numbers, listing components is commonly not too tough to do and also is useful for detect the greatest common factor.

## Listing components to uncover the GCF

To find the greatest typical factor the 8 and 12:

First: perform the factors

 Factors that 8: 1, 2, 4, 8 Factors of 12: 1, 2, 3, 4, 6, 12

Next: to compare these factors and identify the largest aspect that the two numbers share

 The greatest usual factor that 8 and 12 is 4. This can additionally be written as GCF (8, 12) = 4.

## Using element factorization to discover the GCF

To discover the greatest common factor of 36 and also 48,

First: uncover the element factorization

The number 36 and also 48 have the prime components 2, 2, and also 3 in common.

Next: multiply this prime factors: 2 × 2 × 3 = 12

GCF (36, 48) = 12

Knowing how to discover the greatest usual factor is useful in expressing typical fractions in their most basic form.

## Using Euclid"s algorithm to discover the GCF

Prime factorization and listing factors to discover the GCF can conveniently get tedious together the numbers obtain larger. Euclid"s algorithm for finding the GCF is just one of a number of an ext efficient algorithms because that finding the GCF.

Euclid"s algorithm is one algorithm including long division that is based on the principle that the GCF of two numbers doesn"t adjust if the larger number is changed with its difference with the smaller number. So, GCF(18, 34) is the very same as GCF(34 - 18, 18), or GCF(16, 18). We won"t walk into information to prove why the Euclidean algorithm works, however to use the algorithm to discover the GCF, follow this steps:

Divide the smaller sized number (the ahead divisor) through the remainder. If the new remainder is 0, the divisor is the GCF.Continue the procedure of separating the ahead divisor by the remainder until there is no remainder. The divisor that outcomes in a remainder that 0 is the GCF that the original two numbers.

Example

Find GCF(114, 288):

Note the the quotient doesn"t really matter for this algorithm, and we"re no completing the actual initial long department problem.

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After dividing 4 times, the remainder is 0, and the critical divisor is 6. Therefore, based upon the algorithm, GCF(114, 288) = 6. This have the right to be experiment by dividing both 114 and 288 through 6:

114 ÷ 6 = 19

288 ÷ 6 = 48

19 and also 48 don"t share any type of common factors, confirming that 6 is the GCF that 114 and also 288.

This algorithm can additionally be supplied to uncover the GCF for an ext than 2 numbers by finding the GCF in between the first two numbers climate calculating the GCF that the result and the next number. This have the right to be written as: