Greatest Common Factor of 69/31, 54/70, 414/40

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 69/31, 54/70, 414/40

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 69/31,54/70,414/40

Given fractions are 69/31,54/70,414/40

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 69,54,414

Greatest Common Factor of Numerators i.e. GCF of 69,54,414 is 3 .

LCM of Denominators means LCM of 31,70,40 as per the given fractions.

LCM of 31,70,40 is 8680 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 69,54,414

GCF of Fractions 69/31,54/70,414/40 is 3/8680

3 69, 54, 414
23, 18, 138

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 69,54,414 By Matching Biggest Common Factor Method

Greatest Common Factor of 69,54,414 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 54

List of positive integer factors of 54 that divides 54 without a remainder.

1,2,3,6,9,18,27,54

Factors of 414

List of positive integer factors of 414 that divides 414 without a remainder.

1,2,3,6,9,18,23,46,69,138,207,414

Greatest Common Factor

We found the factors 69,54,414 . The biggest common factor number is the GCF number.
So the greatest common factor 69,54,414 is 3.

Lets's calculate LCM of 31,70,40

2 31, 70, 40
5 31, 35, 20
31, 7, 4

∴ So the LCM of the given numbers is 2 x 5 x 31 x 7 x 4 = 8680

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/8680

Therefore, the GCF of Fractions 69/31,54/70,414/40 is 3/8680

Least Common Multiple of 31,70,40 with GCF Formula

Least Common Multiple of 31,70,40 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 31,70,40 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,70,40) = 1

common factors(in case of two or more numbers have common factors) = 10

GCF(31,70,40) x common factors =1 x 10 = 10

LCM(31,70,40) = ( 31 × 70 × 40 ) / 10

LCM(31,70,40) = 86800 / 10

LCM(31,70,40) = 8680


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 69/31, 54/70, 414/40

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 69/31, 54/70, 414/40?

Answer: GCF of Numerators as per given numbers 69/31, 54/70, 414/40 is

GCF of Numerators i.e. for 69,54,414 is 3

LCM of denominators i.e. for 31,70,40 is 8680.

Thus, GCF of Fractions is 3/8680.Finally, GCF of Fractions for 69/31, 54/70, 414/40 is 3/8680.