What is GCF of 21 and 45?
GCF of 21 and 45 is the largest possible number which divides 21 and 45 exactly without any remainder. There are 3 methods commonly used to find the GCF of 21 and 45, i.e. by Euclidean Algorithm, Prime Factorization, or Long Division.
Answer: GCF of 21 and 45 is 3
Explanation:
The GCF of two or more non-zero integers, X (21) and Y (45), is the greatest positive integer M (3), which divides both, X and Y. We can find the GCF of numbers in many ways, the commonly used methods are listed below.
Methods to find GCF of 21 and 45
The methods to compute the GCF of 21 and 45 are explained below.
- By Prime Factorization
- By Euclidean Algorithm
- By Long Division
GCF of 21 and 45 by Prime Factorization
GCF is the product of the factors that are common to each of the given numbers.
- Prime Factorization of 21 is 3 × 7
- Prime Factorization of 45 is 3 × 3 × 5
As visible, 21 and 45 have common prime factors. Here 3 is the only common factor.
Hence, the GCF of 45 and 21 is GCF(21, 45) = GCF(45, 21) = 3
GCF of 21 and 45 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 = 45 and Y = 21,
- GCF(45, 21) = GCF(21, 45 mod 21) = GCF(21, 3)
- GCF(21, 3) = GCF(3, 21 mod 3) = GCF(3, 0)
- GCF(3, 0) = 3 (∵ GCF(X, 0) = X)
Therefore, the GCF of 21 and 45 is 3.
GCF of 21 and 45 by Long Division
GCF is the product of the factors that are common to each of the given numbers.
- Step 1: Divide the larger number by the smaller one.
- Step 2: Divide the dividend by the remainder obtained in Step 1 and repeat this step until we get the remainder as 0.
- Step 3: The last dividend is the GCF of the two numbers.
Here, we take the larger value 45 as the dividend and the smaller value 21 as the divisor.
Therefore, the GCF of 21 and 45 = GCF(21, 45) = GCF(45, 21) = 3.
☛ Also Check:
- GCF of 12, 36 - GCF(12, 36) = 12
- GCF of 14, 49 - GCF(14, 49) = 7
- GCF of 27, 36 - GCF(27, 36) = 9
- GCF of 32, 40 - GCF(32, 40) = 8
- GCF of 30, 40 - GCF(30, 40) = 10
- GCF of 9, 18 - GCF(9, 18) = 9
- GCF of 18, 27 - GCF(18, 27) = 9