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Greatest Common Divisor (GCD) of 117 and 70

The greatest common divisor (GCD) of 117 and 70 is 1.

What is the Greatest Common Divisor (GCD)?

The GCD of two integers is the largest positive integer that divides both numbers without leaving a remainder. It is useful in simplifying fractions, finding common factors, and in number theory.

How to Calculate the GCD of 117 and 70?

We use the Euclidean algorithm, which involves the following steps:

  1. Divide the larger number by the smaller number.
  2. Replace the larger number with the smaller number and the smaller number with the remainder from the division.
  3. Repeat this process until the remainder is zero.
  4. The non-zero remainder just before zero is the GCD.

Step-by-Step Euclidean Algorithm

StepCalculation
1 117 ÷ 70 = 1 remainder 47
2 70 ÷ 47 = 1 remainder 23
3 47 ÷ 23 = 2 remainder 1
4 23 ÷ 1 = 23 remainder 0

Examples of GCD Calculations

NumbersGCD
36 and 1593
172 and 1111
106 and 1622
179 and 1621
168 and 10521

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