Greatest Common Factor of 34/38, 31/98, 72/81, 77/463

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 34/38, 31/98, 72/81, 77/463

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 34/38,31/98,72/81,77/463

Given fractions are 34/38,31/98,72/81,77/463

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 34,31,72,77

Greatest Common Factor of Numerators i.e. GCF of 34,31,72,77 is 1 .

LCM of Denominators means LCM of 38,98,81,463 as per the given fractions.

LCM of 38,98,81,463 is 69830586 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 34,31,72,77

GCF of Fractions 34/38,31/98,72/81,77/463 is 1/69830586

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

Greatest Common Factor of 34,31,72,77 By Matching Biggest Common Factor Method

Greatest Common Factor of 34,31,72,77 By Matching Biggest Common Factor Method

Factors of 34

List of positive integer factors of 34 that divides 34 without a remainder.

1,2,17,34

Factors of 31

List of positive integer factors of 31 that divides 31 without a remainder.

1,31

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 77

List of positive integer factors of 77 that divides 77 without a remainder.

1,7,11,77

Greatest Common Factor

We found the factors 34,31,72,77 . The biggest common factor number is the GCF number.
So the greatest common factor 34,31,72,77 is 1.

Lets's calculate LCM of 38,98,81,463

2 38, 98, 81, 463
19, 49, 81, 463

∴ So the LCM of the given numbers is 2 x 19 x 49 x 81 x 463 = 69830586

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/69830586

Therefore, the GCF of Fractions 34/38,31/98,72/81,77/463 is 1/69830586

Least Common Multiple of 38,98,81,463 with GCF Formula

Least Common Multiple of 38,98,81,463 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 38,98,81,463 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(38,98,81,463) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(38,98,81,463) x common factors =1 x 2 = 2

LCM(38,98,81,463) = ( 38 × 98 × 81 × 463 ) / 2

LCM(38,98,81,463) = 139661172 / 2

LCM(38,98,81,463) = 69830586


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 34/38, 31/98, 72/81, 77/463

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 34/38, 31/98, 72/81, 77/463?

Answer: GCF of Numerators as per given numbers 34/38, 31/98, 72/81, 77/463 is

GCF of Numerators i.e. for 34,31,72,77 is 1

LCM of denominators i.e. for 38,98,81,463 is 69830586.

Thus, GCF of Fractions is 1/69830586.Finally, GCF of Fractions for 34/38, 31/98, 72/81, 77/463 is 1/69830586.