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Greatest Common Divisor (GCD) of 28 and 157

The greatest common divisor (GCD) of 28 and 157 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 28 and 157?

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 28 ÷ 157 = 0 remainder 28
2 157 ÷ 28 = 5 remainder 17
3 28 ÷ 17 = 1 remainder 11
4 17 ÷ 11 = 1 remainder 6
5 11 ÷ 6 = 1 remainder 5
6 6 ÷ 5 = 1 remainder 1
7 5 ÷ 1 = 5 remainder 0

Examples of GCD Calculations

NumbersGCD
199 and 1511
35 and 1005
34 and 222
122 and 1231
175 and 1205

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