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The greatest common divisor(GCD) of 15 and 45 is 15.
What is meant by GCD?
The greatest common divisor (GCD) of two or more integers, where at least one of them is not zero, is the largest positive integer that is a divisor of both numbers. For example, the GCD of 8 and 12 equals 4.
In the divisibility preorder relation, the GCD of a and b is their greatest positive common divisor. This signifies that a and b's common divisors are the same as their GCD divisors. The Euclidean algorithm or Euclid's lemma are widely used to establish this. This is the definition of "greatest" in the context of GCD generalizations.
Foe calculating the GCD of 15 and 45, we have to find the factors of 15 and 45.
Factors of 15:
1, 3, 5, 15
Factors of 45:
1, 3, 5, 9, 15, 45
From all these factors we have to choose the greatest factor that is exactly divisible by both 15 and 45,
So, the greatest factor is 15
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