How to Find GCF of 314/353, 4774/4854?

GCF of 314/353, 4774/4854

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 314/353, 4774/4854 i.e 2/1713462 easily. The following is the detailed procedure to determine the greatest common factor of fractions 314/353, 4774/4854.

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 314/353,4774/4854?

Given fractions are 314/353,4774/4854

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 314/353,4774/4854, numerators are 314,4774

Denominators are 353,4854

The GCF of 314,4774 is 2 .

LCM of 353,4854 is 1713462.

The greatest common factor of 314/353,4774/4854 = [GCF of 314,4774]/[LCM of 353,4854]= 2/1713462

Therefore, the GCF of 314/353,4774/4854 is 2/1713462.

Greatest Common Factor of 314,4774

To find the highest common factor of 314,4774, we have to find the factors of both numbers and list the highest common factor.

The factors of 314 are 1, 2, 157, 314

The factors of 4774 are 1, 2, 7, 11, 14, 22, 31, 62, 77, 154, 217, 341, 434, 682, 2387, 4774

The HCF of 314,4774 is 2.

Lets's calculate GCF of 314,4774

Greatest Common Factor (GCF) of 314,4774 By Common Division

2	314, 4774
	157, 2387

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

Greatest Common Factor of 314,4774 By Matching Biggest Common Factor Method

Now, list down the factors of 314

1,2,157,314

Now, list down the factors of 4774

1,2,7,11,14,22,31,62,77,154,217,341,434,682,2387,4774

Greatest Common Factor

We found the factors 314,4774 . The biggest common factor number is the GCF number.
So the greatest common factor 314,4774 is 2.

Lets's calculate LCM of 353,4854

Lowest Common Multiple of 353,4854 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1713462

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1713462

Therefore, the GCF of Fractions 314/353,4774/4854 is 2/1713462

Least Common Multiple of 353,4854 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 353,4854 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(353,4854) = 1

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

GCF(353,4854) x common factors =1 x 1 = 1

LCM(353,4854) = ( 353 × 4854 ) / 1

LCM(353,4854) = 1713462 / 1

LCM(353,4854) = 1713462

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FAQs on GCF of Fractions of 314/353, 4774/4854

1. What is the HCF of 314,4774?

The HCF of 314,4774 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 314/353, 4774/4854?

Answer: GCF of Numerators as per given numbers 314/353, 4774/4854 is

GCF of Numerators i.e. for 314,4774 is 2

LCM of denominators i.e. for 353,4854 is 1713462.

Thus, GCF of Fractions is 2/1713462.Finally, GCF of Fractions for 314/353, 4774/4854 is 2/1713462.