About gcd calculator
The greatest common divisor (GCD), also called HCF, is the largest number that divides all the given numbers exactly.
Euclid's method
Replace the larger number with the remainder of dividing it by the smaller one, and repeat until the remainder is 0. For 48 and 18: 48 mod 18 = 12, 18 mod 12 = 6, 12 mod 6 = 0, so the GCD is 6.
Uses
Simplifying fractions and ratios, and cutting a length into equal parts of the largest possible size.
A worked example
For 84 and 126, divide 126 by 84 to get a remainder of 42, then divide 84 by 42 to get a remainder of 0. The GCD is 42, so 84/126 simplifies to 2/3.
A practical use
To cut a 84 cm by 126 cm board into the largest identical squares, the side of the square is the GCD, 42 cm, giving 2 × 3 = 6 squares.
