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Greatest Common Divisor (GCD) of 60 and 160

The greatest common divisor (GCD) of 60 and 160 is 20.

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 60 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 60 ÷ 160 = 0 remainder 60
2 160 ÷ 60 = 2 remainder 40
3 60 ÷ 40 = 1 remainder 20
4 40 ÷ 20 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
86 and 462
53 and 201
139 and 611
140 and 822
154 and 357

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