GCF the 48 and also 72 is the largest feasible number the divides 48 and also 72 specifically without any remainder. The determinants of 48 and 72 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 and also 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 respectively. There room 3 typically used approaches to find the GCF that 48 and 72 - long division, prime factorization, and Euclidean algorithm.

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Answer: GCF the 48 and 72 is 24.

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Explanation:

The GCF of 2 non-zero integers, x(48) and y(72), is the biggest positive essence m(24) the divides both x(48) and also y(72) without any kind of remainder.


The techniques to discover the GCF of 48 and 72 are defined below.

Using Euclid's AlgorithmPrime factorization MethodLong division Method

GCF the 48 and also 72 by Euclidean Algorithm

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

Here X = 72 and also Y = 48

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

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

GCF of 48 and 72 by prime Factorization

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Prime administer of 48 and also 72 is (2 × 2 × 2 × 2 × 3) and also (2 × 2 × 2 × 3 × 3) respectively. Together visible, 48 and also 72 have typical prime factors. Hence, the GCF of 48 and 72 is 2 × 2 × 2 × 3 = 24.

GCF of 48 and also 72 by long Division

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GCF that 48 and also 72 is the divisor the we gain when the remainder becomes 0 after ~ doing long department repeatedly.

Step 2: due to the fact that the remainder ≠ 0, we will certainly divide the divisor of step 1 (48) through 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 also 72.