GCF of 48 and 72 is the largest possible number that divides 48 and 72 exactly without any remainder. The factors of 48 and 72 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 respectively. There are 3 commonly used methods to find the GCF of 48 and 72 - long division, prime factorization, and Euclidean algorithm.

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1.GCF of 48 and 72
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Answer: GCF of 48 and 72 is 24.

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Explanation:

The GCF of two non-zero integers, x(48) and y(72), is the greatest positive integer m(24) that divides both x(48) and y(72) without any remainder.


The methods to find the GCF of 48 and 72 are explained below.

Using Euclid's AlgorithmPrime Factorization MethodLong Division Method

GCF of 48 and 72 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)where X > Y and mod is the modulo operator.

Here X = 72 and Y = 48

GCF(72, 48) = GCF(48, 72 mod 48) = GCF(48, 24)GCF(48, 24) = GCF(24, 48 mod 24) = GCF(24, 0)GCF(24, 0) = 24 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 48 and 72 is 24.

GCF of 48 and 72 by Prime Factorization

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Prime factorization of 48 and 72 is (2 × 2 × 2 × 2 × 3) and (2 × 2 × 2 × 3 × 3) respectively. As visible, 48 and 72 have common prime factors. Hence, the GCF of 48 and 72 is 2 × 2 × 2 × 3 = 24.

GCF of 48 and 72 by Long Division

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GCF of 48 and 72 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (48) by the remainder (24).Step 3: Repeat this process until the remainder = 0.

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The corresponding divisor (24) is the GCF of 48 and 72.