Greatest Common Factor of 61/84, 74/78, 12/65, 23/16

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 61/84, 74/78, 12/65, 23/16

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 61/84,74/78,12/65,23/16

Given fractions are 61/84,74/78,12/65,23/16

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 61,74,12,23

Greatest Common Factor of Numerators i.e. GCF of 61,74,12,23 is 1 .

LCM of Denominators means LCM of 84,78,65,16 as per the given fractions.

LCM of 84,78,65,16 is 21840 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 61,74,12,23

GCF of Fractions 61/84,74/78,12/65,23/16 is 1/21840

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 61,74,12,23 By Matching Biggest Common Factor Method

Greatest Common Factor of 61,74,12,23 By Matching Biggest Common Factor Method

Factors of 61

List of positive integer factors of 61 that divides 61 without a remainder.

1,61

Factors of 74

List of positive integer factors of 74 that divides 74 without a remainder.

1,2,37,74

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1,2,3,4,6,12

Factors of 23

List of positive integer factors of 23 that divides 23 without a remainder.

1,23

Greatest Common Factor

We found the factors 61,74,12,23 . The biggest common factor number is the GCF number.
So the greatest common factor 61,74,12,23 is 1.

Lets's calculate LCM of 84,78,65,16

2 84, 78, 65, 16
2 42, 39, 65, 8
3 21, 39, 65, 4
13 7, 13, 65, 4
7, 1, 5, 4

∴ So the LCM of the given numbers is 2 x 2 x 3 x 13 x 7 x 1 x 5 x 4 = 21840

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/21840

Therefore, the GCF of Fractions 61/84,74/78,12/65,23/16 is 1/21840

Least Common Multiple of 84,78,65,16 with GCF Formula

Least Common Multiple of 84,78,65,16 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 84,78,65,16 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(84,78,65,16) = 1

common factors(in case of two or more numbers have common factors) = 312

GCF(84,78,65,16) x common factors =1 x 312 = 312

LCM(84,78,65,16) = ( 84 × 78 × 65 × 16 ) / 312

LCM(84,78,65,16) = 6814080 / 312

LCM(84,78,65,16) = 21840


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 61/84, 74/78, 12/65, 23/16

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 61/84, 74/78, 12/65, 23/16?

Answer: GCF of Numerators as per given numbers 61/84, 74/78, 12/65, 23/16 is

GCF of Numerators i.e. for 61,74,12,23 is 1

LCM of denominators i.e. for 84,78,65,16 is 21840.

Thus, GCF of Fractions is 1/21840.Finally, GCF of Fractions for 61/84, 74/78, 12/65, 23/16 is 1/21840.