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Greatest Common Divisor (GCD) of 117 and 151

The greatest common divisor (GCD) of 117 and 151 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 151?

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 ÷ 151 = 0 remainder 117
2 151 ÷ 117 = 1 remainder 34
3 117 ÷ 34 = 3 remainder 15
4 34 ÷ 15 = 2 remainder 4
5 15 ÷ 4 = 3 remainder 3
6 4 ÷ 3 = 1 remainder 1
7 3 ÷ 1 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
198 and 851
148 and 331
126 and 1566
65 and 1705
54 and 1571

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