Math, asked by nishta1431, 2 days ago

Find the HIGHEST common factor for 21 and 84

Answers

Answered by vandanathakur822
3

Please mark me as the brainliest or click on the crown. Explanation:

Explanation:

The GCF of two non-zero integers, x(21) and y(84), is the greatest positive integer m(21) that divides both x(21) and y(84) without any remainder.

Methods to Find GCF of 21 and 84

The methods to find the GCF of 21 and 84 are explained below.

Using Euclid's Algorithm

Prime Factorization Method

Listing Common Factors

GCF of 21 and 84 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 = 84 and Y = 21

GCF(84, 21) = GCF(21, 84 mod 21) = GCF(21, 0)

GCF(21, 0) = 21 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 21 and 84 is 21.

GCF of 21 and 84 by Prime Factorization

Prime factorization of 21 and 84 is (3 × 7) and (2 × 2 × 3 × 7) respectively. As visible, 21 and 84 have common prime factors. Hence, the GCF of 21 and 84 is 3 × 7 = 21.

GCF of 21 and 84 by Listing Common Factors

GCF of 21 and 84 by Listing Common Factors

Factors of 21: 1, 3, 7, 21

Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

There are 4 common factors of 21 and 84, that are 1, 3, 21, and 7. Therefore, the greatest common factor of 21 and 84 is 21

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