How to Find GCF of 61/217, 76/996, 113/214?

GCF of 61/217, 76/996, 113/214

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 61/217, 76/996, 113/214 i.e 1/23126124 easily. The following is the detailed procedure to determine the greatest common factor of fractions 61/217, 76/996, 113/214.

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 61/217,76/996,113/214?

Given fractions are 61/217,76/996,113/214

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 61/217,76/996,113/214, numerators are 61,76,113

Denominators are 217,996,214

The GCF of 61,76,113 is 1 .

LCM of 217,996,214 is 23126124.

The greatest common factor of 61/217,76/996,113/214 = [GCF of 61,76,113]/[LCM of 217,996,214]= 1/23126124

Therefore, the GCF of 61/217,76/996,113/214 is 1/23126124.

Greatest Common Factor of 61,76,113

To find the highest common factor of 61,76,113, we have to find the factors of both numbers and list the highest common factor.

The factors of 61 are 1, 61

The factors of 76 are 1, 2, 4, 19, 38, 76

The factors of 113 are 1, 113

The HCF of 61,76,113 is 1.

Lets's calculate GCF of 61,76,113

Greatest Common Factor (GCF) of 61,76,113 By Common Division

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

Greatest Common Factor of 61,76,113 By Matching Biggest Common Factor Method

Now, list down the factors of 61

1,61

Now, list down the factors of 76

1,2,4,19,38,76

Now, list down the factors of 113

1,113

Greatest Common Factor

We found the factors 61,76,113 . The biggest common factor number is the GCF number.
So the greatest common factor 61,76,113 is 1.

Lets's calculate LCM of 217,996,214

Lowest Common Multiple of 217,996,214 using Common Division

2	217, 996, 214
	217, 498, 107

∴ So the LCM of the given numbers is 2 x 217 x 498 x 107 = 23126124

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/23126124

Therefore, the GCF of Fractions 61/217,76/996,113/214 is 1/23126124

Least Common Multiple of 217,996,214 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 217,996,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(217,996,214) = 1

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

GCF(217,996,214) x common factors =1 x 2 = 2

LCM(217,996,214) = ( 217 × 996 × 214 ) / 2

LCM(217,996,214) = 46252248 / 2

LCM(217,996,214) = 23126124

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FAQs on GCF of Fractions of 61/217, 76/996, 113/214

1. What is the HCF of 61,76,113?

The HCF of 61,76,113 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 61/217, 76/996, 113/214?

Answer: GCF of Numerators as per given numbers 61/217, 76/996, 113/214 is

GCF of Numerators i.e. for 61,76,113 is 1

LCM of denominators i.e. for 217,996,214 is 23126124.

Thus, GCF of Fractions is 1/23126124.Finally, GCF of Fractions for 61/217, 76/996, 113/214 is 1/23126124.