Greatest Common Factor of 516/414, 3414/802

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 516/414, 3414/802

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 516/414,3414/802

Given fractions are 516/414,3414/802

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 516,3414

Greatest Common Factor of Numerators i.e. GCF of 516,3414 is 6 .

LCM of Denominators means LCM of 414,802 as per the given fractions.

LCM of 414,802 is 166014 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 516,3414

GCF of Fractions 516/414,3414/802 is 6/166014

2 516, 3414
3 258, 1707
86, 569

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 516,3414 By Matching Biggest Common Factor Method

Greatest Common Factor of 516,3414 By Matching Biggest Common Factor Method

Factors of 516

List of positive integer factors of 516 that divides 516 without a remainder.

1,2,3,4,6,12,43,86,129,172,258,516

Factors of 3414

List of positive integer factors of 3414 that divides 3414 without a remainder.

1,2,3,6,569,1138,1707,3414

Greatest Common Factor

We found the factors 516,3414 . The biggest common factor number is the GCF number.
So the greatest common factor 516,3414 is 6.

Lets's calculate LCM of 414,802

2 414, 802
207, 401

∴ So the LCM of the given numbers is 2 x 207 x 401 = 166014

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/166014

Therefore, the GCF of Fractions 516/414,3414/802 is 6/166014

Least Common Multiple of 414,802 with GCF Formula

Least Common Multiple of 414,802 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 414,802 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(414,802) = 2

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

GCF(414,802) x common factors =2 x 1 = 2

LCM(414,802) = ( 414 × 802 ) / 2

LCM(414,802) = 332028 / 2

LCM(414,802) = 166014


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 516/414, 3414/802

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 516/414, 3414/802?

Answer: GCF of Numerators as per given numbers 516/414, 3414/802 is

GCF of Numerators i.e. for 516,3414 is 6

LCM of denominators i.e. for 414,802 is 166014.

Thus, GCF of Fractions is 6/166014.Finally, GCF of Fractions for 516/414, 3414/802 is 6/166014.