How to Find GCF of 14/31, 303/77, 296/715?

GCF of 14/31, 303/77, 296/715

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 14/31, 303/77, 296/715 i.e 1/155155 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/31, 303/77, 296/715.

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 14/31,303/77,296/715?

Given fractions are 14/31,303/77,296/715

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 14/31,303/77,296/715, numerators are 14,303,296

Denominators are 31,77,715

The GCF of 14,303,296 is 1 .

LCM of 31,77,715 is 155155.

The greatest common factor of 14/31,303/77,296/715 = [GCF of 14,303,296]/[LCM of 31,77,715]= 1/155155

Therefore, the GCF of 14/31,303/77,296/715 is 1/155155.

Greatest Common Factor of 14,303,296

To find the highest common factor of 14,303,296, we have to find the factors of both numbers and list the highest common factor.

The factors of 14 are 1, 2, 7, 14

The factors of 303 are 1, 3, 101, 303

The factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296

The HCF of 14,303,296 is 1.

Lets's calculate GCF of 14,303,296

Greatest Common Factor (GCF) of 14,303,296 By Common Division

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

Greatest Common Factor of 14,303,296 By Matching Biggest Common Factor Method

Now, list down the factors of 14

1,2,7,14

Now, list down the factors of 303

1,3,101,303

Now, list down the factors of 296

1,2,4,8,37,74,148,296

Greatest Common Factor

We found the factors 14,303,296 . The biggest common factor number is the GCF number.
So the greatest common factor 14,303,296 is 1.

Lets's calculate LCM of 31,77,715

Lowest Common Multiple of 31,77,715 using Common Division

11	31, 77, 715
	31, 7, 65

∴ So the LCM of the given numbers is 11 x 31 x 7 x 65 = 155155

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/155155

Therefore, the GCF of Fractions 14/31,303/77,296/715 is 1/155155

Least Common Multiple of 31,77,715 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 31,77,715 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,77,715) = 1

common factors(in case of two or more numbers have common factors) = 11

GCF(31,77,715) x common factors =1 x 11 = 11

LCM(31,77,715) = ( 31 × 77 × 715 ) / 11

LCM(31,77,715) = 1706705 / 11

LCM(31,77,715) = 155155

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FAQs on GCF of Fractions of 14/31, 303/77, 296/715

1. What is the HCF of 14,303,296?

The HCF of 14,303,296 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 14/31, 303/77, 296/715?

Answer: GCF of Numerators as per given numbers 14/31, 303/77, 296/715 is

GCF of Numerators i.e. for 14,303,296 is 1

LCM of denominators i.e. for 31,77,715 is 155155.

Thus, GCF of Fractions is 1/155155.Finally, GCF of Fractions for 14/31, 303/77, 296/715 is 1/155155.