How to Find GCF of 7708/970, 7378/350?

GCF of 7708/970, 7378/350

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 7708/970, 7378/350 i.e 2/33950 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7708/970, 7378/350.

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 7708/970,7378/350?

Given fractions are 7708/970,7378/350

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 7708/970,7378/350, numerators are 7708,7378

Denominators are 970,350

The GCF of 7708,7378 is 2 .

LCM of 970,350 is 33950.

The greatest common factor of 7708/970,7378/350 = [GCF of 7708,7378]/[LCM of 970,350]= 2/33950

Therefore, the GCF of 7708/970,7378/350 is 2/33950.

Greatest Common Factor of 7708,7378

To find the highest common factor of 7708,7378, we have to find the factors of both numbers and list the highest common factor.

The factors of 7708 are 1, 2, 4, 41, 47, 82, 94, 164, 188, 1927, 3854, 7708

The factors of 7378 are 1, 2, 7, 14, 17, 31, 34, 62, 119, 217, 238, 434, 527, 1054, 3689, 7378

The HCF of 7708,7378 is 2.

Lets's calculate GCF of 7708,7378

Greatest Common Factor (GCF) of 7708,7378 By Common Division

2	7708, 7378
	3854, 3689

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

Greatest Common Factor of 7708,7378 By Matching Biggest Common Factor Method

Now, list down the factors of 7708

1,2,4,41,47,82,94,164,188,1927,3854,7708

Now, list down the factors of 7378

1,2,7,14,17,31,34,62,119,217,238,434,527,1054,3689,7378

Greatest Common Factor

We found the factors 7708,7378 . The biggest common factor number is the GCF number.
So the greatest common factor 7708,7378 is 2.

Lets's calculate LCM of 970,350

Lowest Common Multiple of 970,350 using Common Division

2	970, 350
5	485, 175
	97, 35

∴ So the LCM of the given numbers is 2 x 5 x 97 x 35 = 33950

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/33950

Therefore, the GCF of Fractions 7708/970,7378/350 is 2/33950

Least Common Multiple of 970,350 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 970,350 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(970,350) = 10

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

GCF(970,350) x common factors =10 x 1 = 10

LCM(970,350) = ( 970 × 350 ) / 10

LCM(970,350) = 339500 / 10

LCM(970,350) = 33950

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FAQs on GCF of Fractions of 7708/970, 7378/350

1. What is the HCF of 7708,7378?

The HCF of 7708,7378 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 7708/970, 7378/350?

Answer: GCF of Numerators as per given numbers 7708/970, 7378/350 is

GCF of Numerators i.e. for 7708,7378 is 2

LCM of denominators i.e. for 970,350 is 33950.

Thus, GCF of Fractions is 2/33950.Finally, GCF of Fractions for 7708/970, 7378/350 is 2/33950.