GCD function: simplify aspect ratios and find largest equal batch sizes

Reduce pixel dimensions or mix ratios automatically

GCD(number1, [number2], ...) returns the largest integer that divides every input without a remainder. Dividing both sides of a 1920 x 1080 display by GCD(1920, 1080) = 120 reduces the resolution cleanly to "16:9".

In warehouse kitting, GCD(240, 180, 300) = 60 tells you the maximum number of identical combo kits you can assemble with zero leftover parts.

Build a live simplified ratio string

Divide Width and Height by GCD(A2, B2) and join them with ":" to display the reduced integer ratio.

Use nonnegative integer dimensions and reject the all-zero pair before dividing by GCD; GCD(0,0)=0 cannot be used as a divisor. Decimal measurements require an agreed integer unit first.

=(A2 / GCD(A2, B2)) & ":" & (B2 / GCD(A2, B2))

Zero and negative input rules

GCD(0, n) returns n, and GCD(0, 0) returns 0. Because divisors of ratios are defined on non-negative integers in spreadsheets, guard negative inputs with IF(MIN(A2, B2)<0, ...).

=IF(MIN(A2, B2)<0, "Non-negative only", GCD(A2, B2))

Further reading

• Microsoft Support — GCD function