How to Find GCF of 312/83, 754/6895?

GCF of 312/83, 754/6895

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 312/83, 754/6895 i.e 26/572285 easily. The following is the detailed procedure to determine the greatest common factor of fractions 312/83, 754/6895.

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 312/83,754/6895?

Given fractions are 312/83,754/6895

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 312/83,754/6895, numerators are 312,754

Denominators are 83,6895

The GCF of 312,754 is 26 .

LCM of 83,6895 is 572285.

The greatest common factor of 312/83,754/6895 = [GCF of 312,754]/[LCM of 83,6895]= 26/572285

Therefore, the GCF of 312/83,754/6895 is 26/572285.

Greatest Common Factor of 312,754

To find the highest common factor of 312,754, we have to find the factors of both numbers and list the highest common factor.

The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312

The factors of 754 are 1, 2, 13, 26, 29, 58, 377, 754

The HCF of 312,754 is 26.

Lets's calculate GCF of 312,754

Greatest Common Factor (GCF) of 312,754 By Common Division

2	312, 754
13	156, 377
	12, 29

∴ So the GCF of the given numbers is 2 x 13 = 26

Greatest Common Factor of 312,754 By Matching Biggest Common Factor Method

Now, list down the factors of 312

1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312

Now, list down the factors of 754

1,2,13,26,29,58,377,754

Greatest Common Factor

We found the factors 312,754 . The biggest common factor number is the GCF number.
So the greatest common factor 312,754 is 26.

Lets's calculate LCM of 83,6895

Lowest Common Multiple of 83,6895 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 572285

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 26/572285

Therefore, the GCF of Fractions 312/83,754/6895 is 26/572285

Least Common Multiple of 83,6895 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 83,6895 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(83,6895) = 1

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

GCF(83,6895) x common factors =1 x 1 = 1

LCM(83,6895) = ( 83 × 6895 ) / 1

LCM(83,6895) = 572285 / 1

LCM(83,6895) = 572285

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FAQs on GCF of Fractions of 312/83, 754/6895

1. What is the HCF of 312,754?

The HCF of 312,754 is 26

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 312/83, 754/6895?

Answer: GCF of Numerators as per given numbers 312/83, 754/6895 is

GCF of Numerators i.e. for 312,754 is 26

LCM of denominators i.e. for 83,6895 is 572285.

Thus, GCF of Fractions is 26/572285.Finally, GCF of Fractions for 312/83, 754/6895 is 26/572285.