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GCF of 872/20, 208/378

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 872/20, 208/378 i.e 8/3780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 872/20, 208/378.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 872/20,208/378?

Given fractions are 872/20,208/378

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 872/20,208/378, numerators are 872,208

Denominators are 20,378

The GCF of 872,208 is 8 .

LCM of 20,378 is 3780.

The greatest common factor of 872/20,208/378 = [GCF of 872,208]/[LCM of 20,378]= 8/3780

Therefore, the GCF of 872/20,208/378 is 8/3780.

Greatest Common Factor of 872,208

To find the highest common factor of 872,208, we have to find the factors of both numbers and list the highest common factor.

The factors of 872 are 1, 2, 4, 8, 109, 218, 436, 872

The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208

The HCF of 872,208 is 8.

Lets's calculate GCF of 872,208

Greatest Common Factor (GCF) of 872,208 By Common Division

2 872, 208
2 436, 104
2 218, 52
109, 26

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 872,208 By Matching Biggest Common Factor Method

Greatest Common Factor of 872,208 By Matching Biggest Common Factor Method

Now, list down the factors of 872

:

1,2,4,8,109,218,436,872

Now, list down the factors of 208

:

1,2,4,8,13,16,26,52,104,208

Greatest Common Factor

We found the factors 872,208 . The biggest common factor number is the GCF number.
So the greatest common factor 872,208 is 8.

Lets's calculate LCM of 20,378

Lowest Common Multiple of 20,378 using Common Division

2 20, 378
10, 189

∴ So the LCM of the given numbers is 2 x 10 x 189 = 3780

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/3780

Therefore, the GCF of Fractions 872/20,208/378 is 8/3780

Least Common Multiple of 20,378 with GCF Formula

Least Common Multiple of 20,378 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 20,378 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(20,378) = 2

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

GCF(20,378) x common factors =2 x 1 = 2

LCM(20,378) = ( 20 × 378 ) / 2

LCM(20,378) = 7560 / 2

LCM(20,378) = 3780


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FAQs on GCF of Fractions of 872/20, 208/378

1. What is the HCF of 872,208?

The HCF of 872,208 is 8

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. 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.

4. What is the GCF of Fractions for 872/20, 208/378?

Answer: GCF of Numerators as per given numbers 872/20, 208/378 is

GCF of Numerators i.e. for 872,208 is 8

LCM of denominators i.e. for 20,378 is 3780.

Thus, GCF of Fractions is 8/3780.Finally, GCF of Fractions for 872/20, 208/378 is 8/3780.