Greatest Common Factor of 21/48, 56/43, 406/105

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 21/48, 56/43, 406/105

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

Greatest Common Factor of 21/48,56/43,406/105

Given fractions are 21/48,56/43,406/105

Formula to find GCF of Fractions is

GCF = GCF of Numerators/LCM of Denominators

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 21,56,406

Greatest Common Factor of Numerators i.e. GCF of 21,56,406 is 7 .

LCM of Denominators means LCM of 48,43,105 as per the given fractions.

LCM of 48,43,105 is 72240 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 21,56,406

GCF of Fractions 21/48,56/43,406/105 is 7/72240

7 21, 56, 406
3, 8, 58

∴ So the GCF of the given numbers is 7 = 7

Greatest Common Factor of 21,56,406 By Matching Biggest Common Factor Method

Greatest Common Factor of 21,56,406 By Matching Biggest Common Factor Method

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1,3,7,21

Factors of 56

List of positive integer factors of 56 that divides 56 without a remainder.

1,2,4,7,8,14,28,56

Factors of 406

List of positive integer factors of 406 that divides 406 without a remainder.

1,2,7,14,29,58,203,406

Greatest Common Factor

We found the factors 21,56,406 . The biggest common factor number is the GCF number.
So the greatest common factor 21,56,406 is 7.

Lets's calculate LCM of 48,43,105

3 48, 43, 105
16, 43, 35

∴ So the LCM of the given numbers is 3 x 16 x 43 x 35 = 72240

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/72240

Therefore, the GCF of Fractions 21/48,56/43,406/105 is 7/72240

Least Common Multiple of 48,43,105 with GCF Formula

Least Common Multiple of 48,43,105 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 48,43,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(48,43,105) = 1

common factors(in case of two or more numbers have common factors) = 3

GCF(48,43,105) x common factors =1 x 3 = 3

LCM(48,43,105) = ( 48 × 43 × 105 ) / 3

LCM(48,43,105) = 216720 / 3

LCM(48,43,105) = 72240


GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 21/48, 56/43, 406/105

1. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

2. What is the GCF of Fractions for 21/48, 56/43, 406/105?

Answer: GCF of Numerators as per given numbers 21/48, 56/43, 406/105 is

GCF of Numerators i.e. for 21,56,406 is 7

LCM of denominators i.e. for 48,43,105 is 72240.

Thus, GCF of Fractions is 7/72240.Finally, GCF of Fractions for 21/48, 56/43, 406/105 is 7/72240.