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GCF of 667/77, 369/978

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 667/77, 369/978 i.e 1/75306 easily. The following is the detailed procedure to determine the greatest common factor of fractions 667/77, 369/978.

Enter two or more fractions separated by "commas"

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

GCF of:

What is the GCF of 667/77,369/978?

Given fractions are 667/77,369/978

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 667/77,369/978, numerators are 667,369

Denominators are 77,978

The GCF of 667,369 is 1 .

LCM of 77,978 is 75306.

The greatest common factor of 667/77,369/978 = [GCF of 667,369]/[LCM of 77,978]= 1/75306

Therefore, the GCF of 667/77,369/978 is 1/75306.

Greatest Common Factor of 667,369

To find the highest common factor of 667,369, we have to find the factors of both numbers and list the highest common factor.

The factors of 667 are 1, 23, 29, 667

The factors of 369 are 1, 3, 9, 41, 123, 369

The HCF of 667,369 is 1.

Lets's calculate GCF of 667,369

Greatest Common Factor (GCF) of 667,369 By Common Division

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

Greatest Common Factor of 667,369 By Matching Biggest Common Factor Method

Greatest Common Factor of 667,369 By Matching Biggest Common Factor Method

Now, list down the factors of 667

:

1,23,29,667

Now, list down the factors of 369

:

1,3,9,41,123,369

Greatest Common Factor

We found the factors 667,369 . The biggest common factor number is the GCF number.
So the greatest common factor 667,369 is 1.

Lets's calculate LCM of 77,978

Lowest Common Multiple of 77,978 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 75306

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/75306

Therefore, the GCF of Fractions 667/77,369/978 is 1/75306

Least Common Multiple of 77,978 with GCF Formula

Least Common Multiple of 77,978 with GCF Formula

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

We need to calculate greatest common factor of 77,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(77,978) = 1

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

GCF(77,978) x common factors =1 x 1 = 1

LCM(77,978) = ( 77 × 978 ) / 1

LCM(77,978) = 75306 / 1

LCM(77,978) = 75306


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FAQs on GCF of Fractions of 667/77, 369/978

1. What is the HCF of 667,369?

The HCF of 667,369 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 667/77, 369/978?

Answer: GCF of Numerators as per given numbers 667/77, 369/978 is

GCF of Numerators i.e. for 667,369 is 1

LCM of denominators i.e. for 77,978 is 75306.

Thus, GCF of Fractions is 1/75306.Finally, GCF of Fractions for 667/77, 369/978 is 1/75306.