How to Find GCF of 9712/852, 6910/461?

GCF of 9712/852, 6910/461

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 9712/852, 6910/461 i.e 2/392772 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9712/852, 6910/461.

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 9712/852,6910/461?

Given fractions are 9712/852,6910/461

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 9712/852,6910/461, numerators are 9712,6910

Denominators are 852,461

The GCF of 9712,6910 is 2 .

LCM of 852,461 is 392772.

The greatest common factor of 9712/852,6910/461 = [GCF of 9712,6910]/[LCM of 852,461]= 2/392772

Therefore, the GCF of 9712/852,6910/461 is 2/392772.

Greatest Common Factor of 9712,6910

To find the highest common factor of 9712,6910, we have to find the factors of both numbers and list the highest common factor.

The factors of 9712 are 1, 2, 4, 8, 16, 607, 1214, 2428, 4856, 9712

The factors of 6910 are 1, 2, 5, 10, 691, 1382, 3455, 6910

The HCF of 9712,6910 is 2.

Lets's calculate GCF of 9712,6910

Greatest Common Factor (GCF) of 9712,6910 By Common Division

2	9712, 6910
	4856, 3455

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

Greatest Common Factor of 9712,6910 By Matching Biggest Common Factor Method

Now, list down the factors of 9712

1,2,4,8,16,607,1214,2428,4856,9712

Now, list down the factors of 6910

1,2,5,10,691,1382,3455,6910

Greatest Common Factor

We found the factors 9712,6910 . The biggest common factor number is the GCF number.
So the greatest common factor 9712,6910 is 2.

Lets's calculate LCM of 852,461

Lowest Common Multiple of 852,461 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 392772

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/392772

Therefore, the GCF of Fractions 9712/852,6910/461 is 2/392772

Least Common Multiple of 852,461 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 852,461 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(852,461) = 1

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

GCF(852,461) x common factors =1 x 1 = 1

LCM(852,461) = ( 852 × 461 ) / 1

LCM(852,461) = 392772 / 1

LCM(852,461) = 392772

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FAQs on GCF of Fractions of 9712/852, 6910/461

1. What is the HCF of 9712,6910?

The HCF of 9712,6910 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 9712/852, 6910/461?

Answer: GCF of Numerators as per given numbers 9712/852, 6910/461 is

GCF of Numerators i.e. for 9712,6910 is 2

LCM of denominators i.e. for 852,461 is 392772.

Thus, GCF of Fractions is 2/392772.Finally, GCF of Fractions for 9712/852, 6910/461 is 2/392772.