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Greatest Common Divisor (GCD) of 70 and 196

The greatest common divisor (GCD) of 70 and 196 is 14.

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 70 and 196?

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 70 ÷ 196 = 0 remainder 70
2 196 ÷ 70 = 2 remainder 56
3 70 ÷ 56 = 1 remainder 14
4 56 ÷ 14 = 4 remainder 0

Examples of GCD Calculations

NumbersGCD
166 and 1351
63 and 1757
98 and 1131
88 and 1531
152 and 871

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