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Greatest Common Divisor (GCD) of 160 and 61

The greatest common divisor (GCD) of 160 and 61 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 160 and 61?

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
1 160 ÷ 61 = 2 remainder 38
2 61 ÷ 38 = 1 remainder 23
3 38 ÷ 23 = 1 remainder 15
4 23 ÷ 15 = 1 remainder 8
5 15 ÷ 8 = 1 remainder 7
6 8 ÷ 7 = 1 remainder 1
7 7 ÷ 1 = 7 remainder 0

Examples of GCD Calculations

NumbersGCD
196 and 1231
27 and 1851
171 and 1191
51 and 1053
183 and 213

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