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To find the greatest common factor (GCF) of 45 and 60, we can use several methods, such as prime factorization, listing factors, or using the Euclidean algorithm. Here, we will use the prime factorization method, which involves expressing both numbers as products of their prime factors and finding the common factors.
To start, we can factor each number into primes:
45 = 3 x 3 x 5
60 = 2 x 2 x 3 x 5
Then, we can identify the common prime factors of the two numbers, which are 3 and 5. The highest power of 3 that divides both 45 and 60 is 3, and the highest power of 5 that divides both is 5. To find the GCF, we multiply these common factors together:
GCF(45, 60) = 3 x 5 = 15
Therefore, the GCF of 45 and 60 is 15.