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GCF of 312/969, 254/741

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 312/969, 254/741 i.e 2/12597 easily. The following is the detailed procedure to determine the greatest common factor of fractions 312/969, 254/741.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 312/969,254/741?

Given fractions are 312/969,254/741

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 312/969,254/741, numerators are 312,254

Denominators are 969,741

The GCF of 312,254 is 2 .

LCM of 969,741 is 12597.

The greatest common factor of 312/969,254/741 = [GCF of 312,254]/[LCM of 969,741]= 2/12597

Therefore, the GCF of 312/969,254/741 is 2/12597.

Greatest Common Factor of 312,254

To find the highest common factor of 312,254, 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 254 are 1, 2, 127, 254

The HCF of 312,254 is 2.

Lets's calculate GCF of 312,254

Greatest Common Factor (GCF) of 312,254 By Common Division

2 312, 254
156, 127

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

Greatest Common Factor of 312,254 By Matching Biggest Common Factor Method

Greatest Common Factor of 312,254 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 254

:

1,2,127,254

Greatest Common Factor

We found the factors 312,254 . The biggest common factor number is the GCF number.
So the greatest common factor 312,254 is 2.

Lets's calculate LCM of 969,741

Lowest Common Multiple of 969,741 using Common Division

3 969, 741
19 323, 247
17, 13

∴ So the LCM of the given numbers is 3 x 19 x 17 x 13 = 12597

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/12597

Therefore, the GCF of Fractions 312/969,254/741 is 2/12597

Least Common Multiple of 969,741 with GCF Formula

Least Common Multiple of 969,741 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 969,741 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(969,741) = 57

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

GCF(969,741) x common factors =57 x 1 = 57

LCM(969,741) = ( 969 × 741 ) / 57

LCM(969,741) = 718029 / 57

LCM(969,741) = 12597


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FAQs on GCF of Fractions of 312/969, 254/741

1. What is the HCF of 312,254?

The HCF of 312,254 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 312/969, 254/741?

Answer: GCF of Numerators as per given numbers 312/969, 254/741 is

GCF of Numerators i.e. for 312,254 is 2

LCM of denominators i.e. for 969,741 is 12597.

Thus, GCF of Fractions is 2/12597.Finally, GCF of Fractions for 312/969, 254/741 is 2/12597.