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GCF of 867/214, 180/236

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 867/214, 180/236 i.e 3/25252 easily. The following is the detailed procedure to determine the greatest common factor of fractions 867/214, 180/236.

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 867/214,180/236?

Given fractions are 867/214,180/236

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 867/214,180/236, numerators are 867,180

Denominators are 214,236

The GCF of 867,180 is 3 .

LCM of 214,236 is 25252.

The greatest common factor of 867/214,180/236 = [GCF of 867,180]/[LCM of 214,236]= 3/25252

Therefore, the GCF of 867/214,180/236 is 3/25252.

Greatest Common Factor of 867,180

To find the highest common factor of 867,180, we have to find the factors of both numbers and list the highest common factor.

The factors of 867 are 1, 3, 17, 51, 289, 867

The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

The HCF of 867,180 is 3.

Lets's calculate GCF of 867,180

Greatest Common Factor (GCF) of 867,180 By Common Division

3 867, 180
289, 60

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 867,180 By Matching Biggest Common Factor Method

Greatest Common Factor of 867,180 By Matching Biggest Common Factor Method

Now, list down the factors of 867

:

1,3,17,51,289,867

Now, list down the factors of 180

:

1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180

Greatest Common Factor

We found the factors 867,180 . The biggest common factor number is the GCF number.
So the greatest common factor 867,180 is 3.

Lets's calculate LCM of 214,236

Lowest Common Multiple of 214,236 using Common Division

2 214, 236
107, 118

∴ So the LCM of the given numbers is 2 x 107 x 118 = 25252

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/25252

Therefore, the GCF of Fractions 867/214,180/236 is 3/25252

Least Common Multiple of 214,236 with GCF Formula

Least Common Multiple of 214,236 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 214,236 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(214,236) = 2

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

GCF(214,236) x common factors =2 x 1 = 2

LCM(214,236) = ( 214 × 236 ) / 2

LCM(214,236) = 50504 / 2

LCM(214,236) = 25252


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FAQs on GCF of Fractions of 867/214, 180/236

1. What is the HCF of 867,180?

The HCF of 867,180 is 3

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 867/214, 180/236?

Answer: GCF of Numerators as per given numbers 867/214, 180/236 is

GCF of Numerators i.e. for 867,180 is 3

LCM of denominators i.e. for 214,236 is 25252.

Thus, GCF of Fractions is 3/25252.Finally, GCF of Fractions for 867/214, 180/236 is 3/25252.