Greatest Common Factor of 378/34, 420/384

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 378/34, 420/384

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 378/34,420/384

Given fractions are 378/34,420/384

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 378,420

Greatest Common Factor of Numerators i.e. GCF of 378,420 is 42 .

LCM of Denominators means LCM of 34,384 as per the given fractions.

LCM of 34,384 is 6528 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 378,420

GCF of Fractions 378/34,420/384 is 42/6528

2 378, 420
3 189, 210
7 63, 70
9, 10

∴ So the GCF of the given numbers is 2 x 3 x 7 = 42

Greatest Common Factor of 378,420 By Matching Biggest Common Factor Method

Greatest Common Factor of 378,420 By Matching Biggest Common Factor Method

Factors of 378

List of positive integer factors of 378 that divides 378 without a remainder.

1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378

Factors of 420

List of positive integer factors of 420 that divides 420 without a remainder.

1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420

Greatest Common Factor

We found the factors 378,420 . The biggest common factor number is the GCF number.
So the greatest common factor 378,420 is 42.

Lets's calculate LCM of 34,384

2 34, 384
17, 192

∴ So the LCM of the given numbers is 2 x 17 x 192 = 6528

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 42/6528

Therefore, the GCF of Fractions 378/34,420/384 is 42/6528

Least Common Multiple of 34,384 with GCF Formula

Least Common Multiple of 34,384 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 34,384 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(34,384) = 2

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

GCF(34,384) x common factors =2 x 1 = 2

LCM(34,384) = ( 34 × 384 ) / 2

LCM(34,384) = 13056 / 2

LCM(34,384) = 6528


GCF of Fractions Calculation Examples

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GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 378/34, 420/384

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 378/34, 420/384?

Answer: GCF of Numerators as per given numbers 378/34, 420/384 is

GCF of Numerators i.e. for 378,420 is 42

LCM of denominators i.e. for 34,384 is 6528.

Thus, GCF of Fractions is 42/6528.Finally, GCF of Fractions for 378/34, 420/384 is 42/6528.