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GCF of 312/950, 259/762

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 312/950, 259/762 i.e 1/361950 easily. The following is the detailed procedure to determine the greatest common factor of fractions 312/950, 259/762.

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 312/950,259/762?

Given fractions are 312/950,259/762

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 312/950,259/762, numerators are 312,259

Denominators are 950,762

The GCF of 312,259 is 1 .

LCM of 950,762 is 361950.

The greatest common factor of 312/950,259/762 = [GCF of 312,259]/[LCM of 950,762]= 1/361950

Therefore, the GCF of 312/950,259/762 is 1/361950.

Greatest Common Factor of 312,259

To find the highest common factor of 312,259, 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 259 are 1, 7, 37, 259

The HCF of 312,259 is 1.

Lets's calculate GCF of 312,259

Greatest Common Factor (GCF) of 312,259 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 312,259 By Matching Biggest Common Factor Method

Greatest Common Factor of 312,259 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 259

:

1,7,37,259

Greatest Common Factor

We found the factors 312,259 . The biggest common factor number is the GCF number.
So the greatest common factor 312,259 is 1.

Lets's calculate LCM of 950,762

Lowest Common Multiple of 950,762 using Common Division

2 950, 762
475, 381

∴ So the LCM of the given numbers is 2 x 475 x 381 = 361950

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/361950

Therefore, the GCF of Fractions 312/950,259/762 is 1/361950

Least Common Multiple of 950,762 with GCF Formula

Least Common Multiple of 950,762 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 950,762 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(950,762) = 2

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

GCF(950,762) x common factors =2 x 1 = 2

LCM(950,762) = ( 950 × 762 ) / 2

LCM(950,762) = 723900 / 2

LCM(950,762) = 361950


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FAQs on GCF of Fractions of 312/950, 259/762

1. What is the HCF of 312,259?

The HCF of 312,259 is 1

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 312/950, 259/762?

Answer: GCF of Numerators as per given numbers 312/950, 259/762 is

GCF of Numerators i.e. for 312,259 is 1

LCM of denominators i.e. for 950,762 is 361950.

Thus, GCF of Fractions is 1/361950.Finally, GCF of Fractions for 312/950, 259/762 is 1/361950.