GCF of 56 and 35 is the largest possible number that divides 56 and 35 exactly without any remainder. The factors of 56 and 35 are 1, 2, 4, 7, 8, 14, 28, 56 and 1, 5, 7, 35 respectively. There are 3 commonly used methods to find the GCF of 56 and 35 - prime factorization, long division, and Euclidean algorithm.

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Answer: GCF of 56 and 35 is 7.

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Explanation:

The GCF of two non-zero integers, x(56) and y(35), is the greatest positive integer m(7) that divides both x(56) and y(35) without any remainder.


The methods to find the GCF of 56 and 35 are explained below.

Long Division MethodPrime Factorization MethodUsing Euclid's Algorithm

GCF of 56 and 35 by Long Division

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GCF of 56 and 35 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 (35) by the remainder (21).Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (7) is the GCF of 56 and 35.

GCF of 56 and 35 by Prime Factorization

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Prime factorization of 56 and 35 is (2 × 2 × 2 × 7) and (5 × 7) respectively. As visible, 56 and 35 have only one common prime factor i.e. 7. Hence, the GCF of 56 and 35 is 7.

GCF of 56 and 35 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.

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Here X = 56 and Y = 35

GCF(56, 35) = GCF(35, 56 mod 35) = GCF(35, 21)GCF(35, 21) = GCF(21, 35 mod 21) = GCF(21, 14)GCF(21, 14) = GCF(14, 21 mod 14) = GCF(14, 7)GCF(14, 7) = GCF(7, 14 mod 7) = GCF(7, 0)GCF(7, 0) = 7 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 56 and 35 is 7.