How to Find GCF of 77/17, 36/109, 678/154?

GCF of 77/17, 36/109, 678/154

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 77/17, 36/109, 678/154 i.e 1/285362 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/17, 36/109, 678/154.

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 77/17,36/109,678/154?

Given fractions are 77/17,36/109,678/154

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 77/17,36/109,678/154, numerators are 77,36,678

Denominators are 17,109,154

The GCF of 77,36,678 is 1 .

LCM of 17,109,154 is 285362.

The greatest common factor of 77/17,36/109,678/154 = [GCF of 77,36,678]/[LCM of 17,109,154]= 1/285362

Therefore, the GCF of 77/17,36/109,678/154 is 1/285362.

Greatest Common Factor of 77,36,678

To find the highest common factor of 77,36,678, 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 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36

The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678

The HCF of 77,36,678 is 1.

Lets's calculate GCF of 77,36,678

Greatest Common Factor (GCF) of 77,36,678 By Common Division

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

Greatest Common Factor of 77,36,678 By Matching Biggest Common Factor Method

Now, list down the factors of 77

1,7,11,77

Now, list down the factors of 36

1,2,3,4,6,9,12,18,36

Now, list down the factors of 678

1,2,3,6,113,226,339,678

Greatest Common Factor

We found the factors 77,36,678 . The biggest common factor number is the GCF number.
So the greatest common factor 77,36,678 is 1.

Lets's calculate LCM of 17,109,154

Lowest Common Multiple of 17,109,154 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 285362

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/285362

Therefore, the GCF of Fractions 77/17,36/109,678/154 is 1/285362

Least Common Multiple of 17,109,154 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 17,109,154 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(17,109,154) = 1

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

GCF(17,109,154) x common factors =1 x 1 = 1

LCM(17,109,154) = ( 17 × 109 × 154 ) / 1

LCM(17,109,154) = 285362 / 1

LCM(17,109,154) = 285362

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FAQs on GCF of Fractions of 77/17, 36/109, 678/154

1. What is the HCF of 77,36,678?

The HCF of 77,36,678 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 77/17, 36/109, 678/154?

Answer: GCF of Numerators as per given numbers 77/17, 36/109, 678/154 is

GCF of Numerators i.e. for 77,36,678 is 1

LCM of denominators i.e. for 17,109,154 is 285362.

Thus, GCF of Fractions is 1/285362.Finally, GCF of Fractions for 77/17, 36/109, 678/154 is 1/285362.