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Greatest Common Divisor (GCD) of 97 and 157

The greatest common divisor (GCD) of 97 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 97 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 97 ÷ 157 = 0 remainder 97
2 157 ÷ 97 = 1 remainder 60
3 97 ÷ 60 = 1 remainder 37
4 60 ÷ 37 = 1 remainder 23
5 37 ÷ 23 = 1 remainder 14
6 23 ÷ 14 = 1 remainder 9
7 14 ÷ 9 = 1 remainder 5
8 9 ÷ 5 = 1 remainder 4
9 5 ÷ 4 = 1 remainder 1
10 4 ÷ 1 = 4 remainder 0

Examples of GCD Calculations

NumbersGCD
123 and 281
165 and 581
17 and 621
54 and 693
166 and 1351

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