How to Find GCF of 78/61, 949/10, 217/518?

GCF of 78/61, 949/10, 217/518

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 78/61, 949/10, 217/518 i.e 1/157990 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/61, 949/10, 217/518.

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 78/61,949/10,217/518?

Given fractions are 78/61,949/10,217/518

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 78/61,949/10,217/518, numerators are 78,949,217

Denominators are 61,10,518

The GCF of 78,949,217 is 1 .

LCM of 61,10,518 is 157990.

The greatest common factor of 78/61,949/10,217/518 = [GCF of 78,949,217]/[LCM of 61,10,518]= 1/157990

Therefore, the GCF of 78/61,949/10,217/518 is 1/157990.

Greatest Common Factor of 78,949,217

To find the highest common factor of 78,949,217, 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 949 are 1, 13, 73, 949

The factors of 217 are 1, 7, 31, 217

The HCF of 78,949,217 is 1.

Lets's calculate GCF of 78,949,217

Greatest Common Factor (GCF) of 78,949,217 By Common Division

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

Greatest Common Factor of 78,949,217 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 949

1,13,73,949

Now, list down the factors of 217

1,7,31,217

Greatest Common Factor

We found the factors 78,949,217 . The biggest common factor number is the GCF number.
So the greatest common factor 78,949,217 is 1.

Lets's calculate LCM of 61,10,518

Lowest Common Multiple of 61,10,518 using Common Division

2	61, 10, 518
	61, 5, 259

∴ So the LCM of the given numbers is 2 x 61 x 5 x 259 = 157990

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/157990

Therefore, the GCF of Fractions 78/61,949/10,217/518 is 1/157990

Least Common Multiple of 61,10,518 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 61,10,518 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(61,10,518) = 1

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

GCF(61,10,518) x common factors =1 x 2 = 2

LCM(61,10,518) = ( 61 × 10 × 518 ) / 2

LCM(61,10,518) = 315980 / 2

LCM(61,10,518) = 157990

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 78/61, 949/10, 217/518

1. What is the HCF of 78,949,217?

The HCF of 78,949,217 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 78/61, 949/10, 217/518?

Answer: GCF of Numerators as per given numbers 78/61, 949/10, 217/518 is

GCF of Numerators i.e. for 78,949,217 is 1

LCM of denominators i.e. for 61,10,518 is 157990.

Thus, GCF of Fractions is 1/157990.Finally, GCF of Fractions for 78/61, 949/10, 217/518 is 1/157990.