Cryptography

Public Key Cryptography: GCD plays a crucial role in algorithms like RSA, which is widely used for secure data transmission. RSA involves finding large prime numbers, and the GCD is used to ensure that certain key values are co-prime (i.e., their GCD is 1). Digital Signal Processing

Sampling Rates: In audio or video signal processing, different devices may use different sampling rates. GCD is used to find the highest possible common sampling rate, allowing for proper synchronization between devices. Fractions and Ratios

Simplifying Fractions: In everyday situations, such as cooking or measurements, GCD helps simplify fractions. For example, if a recipe calls for 4/8 of a cup, knowing the GCD (which is 4) allows simplification to 1/2. Time and Frequency Alignment

Synchronization: GCD can be used to align cycles or frequencies in mechanical systems (like gears) or digital clocks. For example, if two events repeat every 15 and 20 minutes, the GCD (5 minutes) gives the interval when both events will occur simultaneously.