How to Find GCF of 80/214, 67/190, 218/872?

GCF of 80/214, 67/190, 218/872

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 80/214, 67/190, 218/872 i.e 1/8863880 easily. The following is the detailed procedure to determine the greatest common factor of fractions 80/214, 67/190, 218/872.

Enter two or more fractions separated by "commas"

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

What is the GCF of 80/214,67/190,218/872?

Given fractions are 80/214,67/190,218/872

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 80/214,67/190,218/872, numerators are 80,67,218

Denominators are 214,190,872

The GCF of 80,67,218 is 1 .

LCM of 214,190,872 is 8863880.

The greatest common factor of 80/214,67/190,218/872 = [GCF of 80,67,218]/[LCM of 214,190,872]= 1/8863880

Therefore, the GCF of 80/214,67/190,218/872 is 1/8863880.

Greatest Common Factor of 80,67,218

To find the highest common factor of 80,67,218, we have to find the factors of both numbers and list the highest common factor.

The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

The factors of 67 are 1, 67

The factors of 218 are 1, 2, 109, 218

The HCF of 80,67,218 is 1.

Lets's calculate GCF of 80,67,218

Greatest Common Factor (GCF) of 80,67,218 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 80,67,218 By Matching Biggest Common Factor Method

Now, list down the factors of 80

1,2,4,5,8,10,16,20,40,80

Now, list down the factors of 67

1,67

Now, list down the factors of 218

1,2,109,218

Greatest Common Factor

We found the factors 80,67,218 . The biggest common factor number is the GCF number.
So the greatest common factor 80,67,218 is 1.

Lets's calculate LCM of 214,190,872

Lowest Common Multiple of 214,190,872 using Common Division

2	214, 190, 872
	107, 95, 436

∴ So the LCM of the given numbers is 2 x 107 x 95 x 436 = 8863880

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8863880

Therefore, the GCF of Fractions 80/214,67/190,218/872 is 1/8863880

Least Common Multiple of 214,190,872 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 214,190,872 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(214,190,872) = 2

common factors(in case of two or more numbers have common factors) = 2

GCF(214,190,872) x common factors =2 x 2 = 4

LCM(214,190,872) = ( 214 × 190 × 872 ) / 4

LCM(214,190,872) = 35455520 / 4

LCM(214,190,872) = 8863880

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FAQs on GCF of Fractions of 80/214, 67/190, 218/872

1. What is the HCF of 80,67,218?

The HCF of 80,67,218 is 1

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 80/214, 67/190, 218/872?

Answer: GCF of Numerators as per given numbers 80/214, 67/190, 218/872 is

GCF of Numerators i.e. for 80,67,218 is 1

LCM of denominators i.e. for 214,190,872 is 8863880.

Thus, GCF of Fractions is 1/8863880.Finally, GCF of Fractions for 80/214, 67/190, 218/872 is 1/8863880.