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Greatest Common Divisor (GCD) of 46 and 180

The greatest common divisor (GCD) of 46 and 180 is 2.

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 46 and 180?

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 46 ÷ 180 = 0 remainder 46
2 180 ÷ 46 = 3 remainder 42
3 46 ÷ 42 = 1 remainder 4
4 42 ÷ 4 = 10 remainder 2
5 4 ÷ 2 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
141 and 213
32 and 782
112 and 1616
65 and 331
109 and 1731

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