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Greatest Common Divisor (GCD) of 64 and 160

The greatest common divisor (GCD) of 64 and 160 is 32.

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 64 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 64 ÷ 160 = 0 remainder 64
2 160 ÷ 64 = 2 remainder 32
3 64 ÷ 32 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
167 and 1961
33 and 341
189 and 1323
196 and 18214
76 and 684

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