Greatest Common Factor of 514/678, 714/611

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 514/678, 714/611

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 514/678,714/611

Given fractions are 514/678,714/611

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 514,714

Greatest Common Factor of Numerators i.e. GCF of 514,714 is 2 .

LCM of Denominators means LCM of 678,611 as per the given fractions.

LCM of 678,611 is 414258 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 514,714

GCF of Fractions 514/678,714/611 is 2/414258

2 514, 714
257, 357

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 514,714 By Matching Biggest Common Factor Method

Greatest Common Factor of 514,714 By Matching Biggest Common Factor Method

Factors of 514

List of positive integer factors of 514 that divides 514 without a remainder.

1,2,257,514

Factors of 714

List of positive integer factors of 714 that divides 714 without a remainder.

1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714

Greatest Common Factor

We found the factors 514,714 . The biggest common factor number is the GCF number.
So the greatest common factor 514,714 is 2.

Lets's calculate LCM of 678,611

Given numbers has no common factors except 1. So, there LCM is their product i.e 414258

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/414258

Therefore, the GCF of Fractions 514/678,714/611 is 2/414258

Least Common Multiple of 678,611 with GCF Formula

Least Common Multiple of 678,611 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 678,611 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(678,611) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(678,611) x common factors =1 x 1 = 1

LCM(678,611) = ( 678 × 611 ) / 1

LCM(678,611) = 414258 / 1

LCM(678,611) = 414258


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 514/678, 714/611

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 514/678, 714/611?

Answer: GCF of Numerators as per given numbers 514/678, 714/611 is

GCF of Numerators i.e. for 514,714 is 2

LCM of denominators i.e. for 678,611 is 414258.

Thus, GCF of Fractions is 2/414258.Finally, GCF of Fractions for 514/678, 714/611 is 2/414258.