You could use the prime factorization method, which sounds fancy but is just detective work. Break 45 into its secret ingredients: 3 × 3 × 5. Then do the same for 76: 2 × 2 × 19. No matching numbers? Congratulations, you’ve found the GCF of 1.
GCF of 45 and 75 | How to Find GCF of 45, 75?
Or you could use the Euclidean algorithm, which is the ancient Greek version of subtraction-based torture. You subtract 45 from 76 to get 31, then 31 from 45 to get 14, and so on until you land on 1. It’s like peeling an onion of disappointment until you’re left with a single, teary tear of truth.
Fun fact: the Euclidean algorithm is over 2,300 years old. It was discovered by Euclid, a guy who probably never had to calculate a tip at a restaurant. But his method still powers modern cryptography—so thank him next time you buy something online.
