Euclid's Algorithm Calculator

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Euclid's Algorithm GCF Calculator

Value 1:

Value 2:

Answer:

GCF(816, 2260) = 4
Greatest Common Factor

Solution

Set up a division problem (a ÷ b = ?) where a is larger than b.

Do the division a ÷ b = c with remainder R.

Then, replace a with b, replace b with R, and do the new division problem.

Continue the process until R = 0.

2260 ÷ 816 = 2 R 628
   (2260 = 2 × 816 + 628)

816 ÷ 628 = 1 R 188
   (816 = 1 × 628 + 188)

628 ÷ 188 = 3 R 64
   (628 = 3 × 188 + 64)

188 ÷ 64 = 2 R 60
   (188 = 2 × 64 + 60)

64 ÷ 60 = 1 R 4
   (64 = 1 × 60 + 4)

60 ÷ 4 = 15 R 0
   (60 = 15 × 4 + 0)

When remainder R = 0, the GCF is the divisor, b, in the last equation. GCF = 4

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Calculator Use

Enter two whole numbers to find the greatest common factor (GCF). See the work and learn how to find the GCF using the Euclidean Algorithm.

How to Find the GCF Using Euclid's Algorithm

Given two whole numbers where a is greater than b, do the division a ÷ b = c with remainder R.
Replace a with b, replace b with R and repeat the division.
Repeat step 2 until R=0.
When R=0, the divisor, b, in the last equation is the greatest common factor, GCF.

Since greatest common factor (GCF) and greatest common divisor (GCD) are synonymous, the Euclidean Algorithm process also works to find the GCD.

Related Calculators

To find the GCF of more than two values see our Greatest Common Factor Calculator.

For more information and examples using the Euclidean Algorithm see our GCF Calculator and the section on Euclid's Algorithm.

References

Bureau 42: The Euclidean Algorithm: Greatest Common Factors Through Subtraction.

Rutgers University Department of Mathematics: The Euclidean Algorithm.