How to Find GCF of 610/680, 7678/112?

GCF of 610/680, 7678/112

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 610/680, 7678/112 i.e 2/9520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 610/680, 7678/112.

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 610/680,7678/112?

Given fractions are 610/680,7678/112

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 610/680,7678/112, numerators are 610,7678

Denominators are 680,112

The GCF of 610,7678 is 2 .

LCM of 680,112 is 9520.

The greatest common factor of 610/680,7678/112 = [GCF of 610,7678]/[LCM of 680,112]= 2/9520

Therefore, the GCF of 610/680,7678/112 is 2/9520.

Greatest Common Factor of 610,7678

To find the highest common factor of 610,7678, we have to find the factors of both numbers and list the highest common factor.

The factors of 610 are 1, 2, 5, 10, 61, 122, 305, 610

The factors of 7678 are 1, 2, 11, 22, 349, 698, 3839, 7678

The HCF of 610,7678 is 2.

Lets's calculate GCF of 610,7678

Greatest Common Factor (GCF) of 610,7678 By Common Division

2	610, 7678
	305, 3839

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 610,7678 By Matching Biggest Common Factor Method

Now, list down the factors of 610

1,2,5,10,61,122,305,610

Now, list down the factors of 7678

1,2,11,22,349,698,3839,7678

Greatest Common Factor

We found the factors 610,7678 . The biggest common factor number is the GCF number.
So the greatest common factor 610,7678 is 2.

Lets's calculate LCM of 680,112

Lowest Common Multiple of 680,112 using Common Division

2	680, 112
2	340, 56
2	170, 28
	85, 14

∴ So the LCM of the given numbers is 2 x 2 x 2 x 85 x 14 = 9520

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/9520

Therefore, the GCF of Fractions 610/680,7678/112 is 2/9520

Least Common Multiple of 680,112 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 680,112 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(680,112) = 8

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

GCF(680,112) x common factors =8 x 1 = 8

LCM(680,112) = ( 680 × 112 ) / 8

LCM(680,112) = 76160 / 8

LCM(680,112) = 9520

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FAQs on GCF of Fractions of 610/680, 7678/112

1. What is the HCF of 610,7678?

The HCF of 610,7678 is 2

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 610/680, 7678/112?

Answer: GCF of Numerators as per given numbers 610/680, 7678/112 is

GCF of Numerators i.e. for 610,7678 is 2

LCM of denominators i.e. for 680,112 is 9520.

Thus, GCF of Fractions is 2/9520.Finally, GCF of Fractions for 610/680, 7678/112 is 2/9520.