How to Find GCF of 677/214, 208/791?

GCF of 677/214, 208/791

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 677/214, 208/791 i.e 1/169274 easily. The following is the detailed procedure to determine the greatest common factor of fractions 677/214, 208/791.

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 677/214,208/791?

Given fractions are 677/214,208/791

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 677/214,208/791, numerators are 677,208

Denominators are 214,791

The GCF of 677,208 is 1 .

LCM of 214,791 is 169274.

The greatest common factor of 677/214,208/791 = [GCF of 677,208]/[LCM of 214,791]= 1/169274

Therefore, the GCF of 677/214,208/791 is 1/169274.

Greatest Common Factor of 677,208

To find the highest common factor of 677,208, we have to find the factors of both numbers and list the highest common factor.

The factors of 677 are 1, 677

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

The HCF of 677,208 is 1.

Lets's calculate GCF of 677,208

Greatest Common Factor (GCF) of 677,208 By Common Division

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

Greatest Common Factor of 677,208 By Matching Biggest Common Factor Method

Now, list down the factors of 677

1,677

Now, list down the factors of 208

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

Greatest Common Factor

We found the factors 677,208 . The biggest common factor number is the GCF number.
So the greatest common factor 677,208 is 1.

Lets's calculate LCM of 214,791

Lowest Common Multiple of 214,791 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 169274

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/169274

Therefore, the GCF of Fractions 677/214,208/791 is 1/169274

Least Common Multiple of 214,791 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 214,791 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(214,791) = 1

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

GCF(214,791) x common factors =1 x 1 = 1

LCM(214,791) = ( 214 × 791 ) / 1

LCM(214,791) = 169274 / 1

LCM(214,791) = 169274

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FAQs on GCF of Fractions of 677/214, 208/791

1. What is the HCF of 677,208?

The HCF of 677,208 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 677/214, 208/791?

Answer: GCF of Numerators as per given numbers 677/214, 208/791 is

GCF of Numerators i.e. for 677,208 is 1

LCM of denominators i.e. for 214,791 is 169274.

Thus, GCF of Fractions is 1/169274.Finally, GCF of Fractions for 677/214, 208/791 is 1/169274.