Find the HIGHEST common factor for 21 and 84
Answers
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