Greatest Common Factor of 69/40, 72/15, 12/77, 86/305

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 69/40, 72/15, 12/77, 86/305

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 69/40,72/15,12/77,86/305

Given fractions are 69/40,72/15,12/77,86/305

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 69,72,12,86

Greatest Common Factor of Numerators i.e. GCF of 69,72,12,86 is 1 .

LCM of Denominators means LCM of 40,15,77,305 as per the given fractions.

LCM of 40,15,77,305 is 563640 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 69,72,12,86

GCF of Fractions 69/40,72/15,12/77,86/305 is 1/563640

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

Greatest Common Factor of 69,72,12,86 By Matching Biggest Common Factor Method

Greatest Common Factor of 69,72,12,86 By Matching Biggest Common Factor Method

Factors of 69

List of positive integer factors of 69 that divides 69 without a remainder.

1,3,23,69

Factors of 72

List of positive integer factors of 72 that divides 72 without a remainder.

1,2,3,4,6,8,9,12,18,24,36,72

Factors of 12

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

1,2,3,4,6,12

Factors of 86

List of positive integer factors of 86 that divides 86 without a remainder.

1,2,43,86

Greatest Common Factor

We found the factors 69,72,12,86 . The biggest common factor number is the GCF number.
So the greatest common factor 69,72,12,86 is 1.

Lets's calculate LCM of 40,15,77,305

5 40, 15, 77, 305
8, 3, 77, 61

∴ So the LCM of the given numbers is 5 x 8 x 3 x 77 x 61 = 563640

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/563640

Therefore, the GCF of Fractions 69/40,72/15,12/77,86/305 is 1/563640

Least Common Multiple of 40,15,77,305 with GCF Formula

Least Common Multiple of 40,15,77,305 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 40,15,77,305 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(40,15,77,305) = 1

common factors(in case of two or more numbers have common factors) = 25

GCF(40,15,77,305) x common factors =1 x 25 = 25

LCM(40,15,77,305) = ( 40 × 15 × 77 × 305 ) / 25

LCM(40,15,77,305) = 14091000 / 25

LCM(40,15,77,305) = 563640


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 69/40, 72/15, 12/77, 86/305

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 69/40, 72/15, 12/77, 86/305?

Answer: GCF of Numerators as per given numbers 69/40, 72/15, 12/77, 86/305 is

GCF of Numerators i.e. for 69,72,12,86 is 1

LCM of denominators i.e. for 40,15,77,305 is 563640.

Thus, GCF of Fractions is 1/563640.Finally, GCF of Fractions for 69/40, 72/15, 12/77, 86/305 is 1/563640.