How to Find GCF of 78/706, 49/399, 167/284?

GCF of 78/706, 49/399, 167/284

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 78/706, 49/399, 167/284 i.e 1/40000548 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/706, 49/399, 167/284.

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 78/706,49/399,167/284?

Given fractions are 78/706,49/399,167/284

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 78/706,49/399,167/284, numerators are 78,49,167

Denominators are 706,399,284

The GCF of 78,49,167 is 1 .

LCM of 706,399,284 is 40000548.

The greatest common factor of 78/706,49/399,167/284 = [GCF of 78,49,167]/[LCM of 706,399,284]= 1/40000548

Therefore, the GCF of 78/706,49/399,167/284 is 1/40000548.

Greatest Common Factor of 78,49,167

To find the highest common factor of 78,49,167, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 49 are 1, 7, 49

The factors of 167 are 1, 167

The HCF of 78,49,167 is 1.

Lets's calculate GCF of 78,49,167

Greatest Common Factor (GCF) of 78,49,167 By Common Division

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

Greatest Common Factor of 78,49,167 By Matching Biggest Common Factor Method

Now, list down the factors of 78

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

Now, list down the factors of 49

1,7,49

Now, list down the factors of 167

1,167

Greatest Common Factor

We found the factors 78,49,167 . The biggest common factor number is the GCF number.
So the greatest common factor 78,49,167 is 1.

Lets's calculate LCM of 706,399,284

Lowest Common Multiple of 706,399,284 using Common Division

2	706, 399, 284
	353, 399, 142

∴ So the LCM of the given numbers is 2 x 353 x 399 x 142 = 40000548

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/40000548

Therefore, the GCF of Fractions 78/706,49/399,167/284 is 1/40000548

Least Common Multiple of 706,399,284 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 706,399,284 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(706,399,284) = 1

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

GCF(706,399,284) x common factors =1 x 2 = 2

LCM(706,399,284) = ( 706 × 399 × 284 ) / 2

LCM(706,399,284) = 80001096 / 2

LCM(706,399,284) = 40000548

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 78/706, 49/399, 167/284

1. What is the HCF of 78,49,167?

The HCF of 78,49,167 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 78/706, 49/399, 167/284?

Answer: GCF of Numerators as per given numbers 78/706, 49/399, 167/284 is

GCF of Numerators i.e. for 78,49,167 is 1

LCM of denominators i.e. for 706,399,284 is 40000548.

Thus, GCF of Fractions is 1/40000548.Finally, GCF of Fractions for 78/706, 49/399, 167/284 is 1/40000548.