How to Find GCF of 77/129, 31/164, 849/694?

GCF of 77/129, 31/164, 849/694

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 77/129, 31/164, 849/694 i.e 1/7341132 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/129, 31/164, 849/694.

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 77/129,31/164,849/694?

Given fractions are 77/129,31/164,849/694

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 77/129,31/164,849/694, numerators are 77,31,849

Denominators are 129,164,694

The GCF of 77,31,849 is 1 .

LCM of 129,164,694 is 7341132.

The greatest common factor of 77/129,31/164,849/694 = [GCF of 77,31,849]/[LCM of 129,164,694]= 1/7341132

Therefore, the GCF of 77/129,31/164,849/694 is 1/7341132.

Greatest Common Factor of 77,31,849

To find the highest common factor of 77,31,849, we have to find the factors of both numbers and list the highest common factor.

The factors of 77 are 1, 7, 11, 77

The factors of 31 are 1, 31

The factors of 849 are 1, 3, 283, 849

The HCF of 77,31,849 is 1.

Lets's calculate GCF of 77,31,849

Greatest Common Factor (GCF) of 77,31,849 By Common Division

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

Greatest Common Factor of 77,31,849 By Matching Biggest Common Factor Method

Now, list down the factors of 77

1,7,11,77

Now, list down the factors of 31

1,31

Now, list down the factors of 849

1,3,283,849

Greatest Common Factor

We found the factors 77,31,849 . The biggest common factor number is the GCF number.
So the greatest common factor 77,31,849 is 1.

Lets's calculate LCM of 129,164,694

Lowest Common Multiple of 129,164,694 using Common Division

2	129, 164, 694
	129, 82, 347

∴ So the LCM of the given numbers is 2 x 129 x 82 x 347 = 7341132

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7341132

Therefore, the GCF of Fractions 77/129,31/164,849/694 is 1/7341132

Least Common Multiple of 129,164,694 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 129,164,694 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(129,164,694) = 1

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

GCF(129,164,694) x common factors =1 x 2 = 2

LCM(129,164,694) = ( 129 × 164 × 694 ) / 2

LCM(129,164,694) = 14682264 / 2

LCM(129,164,694) = 7341132

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 77/129, 31/164, 849/694

1. What is the HCF of 77,31,849?

The HCF of 77,31,849 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 77/129, 31/164, 849/694?

Answer: GCF of Numerators as per given numbers 77/129, 31/164, 849/694 is

GCF of Numerators i.e. for 77,31,849 is 1

LCM of denominators i.e. for 129,164,694 is 7341132.

Thus, GCF of Fractions is 1/7341132.Finally, GCF of Fractions for 77/129, 31/164, 849/694 is 1/7341132.