How to Find GCF of 26/21, 78/61, 829/691?

GCF of 26/21, 78/61, 829/691

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 26/21, 78/61, 829/691 i.e 1/885171 easily. The following is the detailed procedure to determine the greatest common factor of fractions 26/21, 78/61, 829/691.

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 26/21,78/61,829/691?

Given fractions are 26/21,78/61,829/691

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 26/21,78/61,829/691, numerators are 26,78,829

Denominators are 21,61,691

The GCF of 26,78,829 is 1 .

LCM of 21,61,691 is 885171.

The greatest common factor of 26/21,78/61,829/691 = [GCF of 26,78,829]/[LCM of 21,61,691]= 1/885171

Therefore, the GCF of 26/21,78/61,829/691 is 1/885171.

Greatest Common Factor of 26,78,829

To find the highest common factor of 26,78,829, we have to find the factors of both numbers and list the highest common factor.

The factors of 26 are 1, 2, 13, 26

The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78

The factors of 829 are 1, 829

The HCF of 26,78,829 is 1.

Lets's calculate GCF of 26,78,829

Greatest Common Factor (GCF) of 26,78,829 By Common Division

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

Greatest Common Factor of 26,78,829 By Matching Biggest Common Factor Method

Now, list down the factors of 26

1,2,13,26

Now, list down the factors of 78

1,2,3,6,13,26,39,78

Now, list down the factors of 829

1,829

Greatest Common Factor

We found the factors 26,78,829 . The biggest common factor number is the GCF number.
So the greatest common factor 26,78,829 is 1.

Lets's calculate LCM of 21,61,691

Lowest Common Multiple of 21,61,691 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 885171

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/885171

Therefore, the GCF of Fractions 26/21,78/61,829/691 is 1/885171

Least Common Multiple of 21,61,691 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 21,61,691 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(21,61,691) = 1

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

GCF(21,61,691) x common factors =1 x 1 = 1

LCM(21,61,691) = ( 21 × 61 × 691 ) / 1

LCM(21,61,691) = 885171 / 1

LCM(21,61,691) = 885171

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FAQs on GCF of Fractions of 26/21, 78/61, 829/691

1. What is the HCF of 26,78,829?

The HCF of 26,78,829 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 26/21, 78/61, 829/691?

Answer: GCF of Numerators as per given numbers 26/21, 78/61, 829/691 is

GCF of Numerators i.e. for 26,78,829 is 1

LCM of denominators i.e. for 21,61,691 is 885171.

Thus, GCF of Fractions is 1/885171.Finally, GCF of Fractions for 26/21, 78/61, 829/691 is 1/885171.