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Greatest Common Divisor (GCD) of 59 and 160

The greatest common divisor (GCD) of 59 and 160 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 59 and 160?

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 59 ÷ 160 = 0 remainder 59
2 160 ÷ 59 = 2 remainder 42
3 59 ÷ 42 = 1 remainder 17
4 42 ÷ 17 = 2 remainder 8
5 17 ÷ 8 = 2 remainder 1
6 8 ÷ 1 = 8 remainder 0

Examples of GCD Calculations

NumbersGCD
83 and 1241
98 and 1382
151 and 1441
174 and 1311
61 and 991

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