Greatest Common Factor of 17/82, 74/35, 14/98, 98/410

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 17/82, 74/35, 14/98, 98/410

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 17/82,74/35,14/98,98/410

Given fractions are 17/82,74/35,14/98,98/410

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 17,74,14,98

Greatest Common Factor of Numerators i.e. GCF of 17,74,14,98 is 1 .

LCM of Denominators means LCM of 82,35,98,410 as per the given fractions.

LCM of 82,35,98,410 is 20090 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 17,74,14,98

GCF of Fractions 17/82,74/35,14/98,98/410 is 1/20090

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

Greatest Common Factor of 17,74,14,98 By Matching Biggest Common Factor Method

Greatest Common Factor of 17,74,14,98 By Matching Biggest Common Factor Method

Factors of 17

List of positive integer factors of 17 that divides 17 without a remainder.

1,17

Factors of 74

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

1,2,37,74

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1,2,7,14

Factors of 98

List of positive integer factors of 98 that divides 98 without a remainder.

1,2,7,14,49,98

Greatest Common Factor

We found the factors 17,74,14,98 . The biggest common factor number is the GCF number.
So the greatest common factor 17,74,14,98 is 1.

Lets's calculate LCM of 82,35,98,410

2 82, 35, 98, 410
5 41, 35, 49, 205
7 41, 7, 49, 41
41 41, 1, 7, 41
1, 1, 7, 1

∴ So the LCM of the given numbers is 2 x 5 x 7 x 41 x 1 x 1 x 7 x 1 = 20090

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/20090

Therefore, the GCF of Fractions 17/82,74/35,14/98,98/410 is 1/20090

Least Common Multiple of 82,35,98,410 with GCF Formula

Least Common Multiple of 82,35,98,410 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 82,35,98,410 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(82,35,98,410) = 1

common factors(in case of two or more numbers have common factors) = 5740

GCF(82,35,98,410) x common factors =1 x 5740 = 5740

LCM(82,35,98,410) = ( 82 × 35 × 98 × 410 ) / 5740

LCM(82,35,98,410) = 115316600 / 5740

LCM(82,35,98,410) = 20090


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 17/82, 74/35, 14/98, 98/410

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 17/82, 74/35, 14/98, 98/410?

Answer: GCF of Numerators as per given numbers 17/82, 74/35, 14/98, 98/410 is

GCF of Numerators i.e. for 17,74,14,98 is 1

LCM of denominators i.e. for 82,35,98,410 is 20090.

Thus, GCF of Fractions is 1/20090.Finally, GCF of Fractions for 17/82, 74/35, 14/98, 98/410 is 1/20090.