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Greatest Common Divisor (GCD) of 17 and 40

The greatest common divisor (GCD) of 17 and 40 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 17 and 40?

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 17 ÷ 40 = 0 remainder 17
2 40 ÷ 17 = 2 remainder 6
3 17 ÷ 6 = 2 remainder 5
4 6 ÷ 5 = 1 remainder 1
5 5 ÷ 1 = 5 remainder 0

Examples of GCD Calculations

NumbersGCD
132 and 8412
181 and 251
50 and 4010
66 and 1571
11 and 161

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