How to Find GCF of 464/314, 6716/8242?

GCF of 464/314, 6716/8242

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 464/314, 6716/8242 i.e 4/1293994 easily. The following is the detailed procedure to determine the greatest common factor of fractions 464/314, 6716/8242.

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 464/314,6716/8242?

Given fractions are 464/314,6716/8242

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 464/314,6716/8242, numerators are 464,6716

Denominators are 314,8242

The GCF of 464,6716 is 4 .

LCM of 314,8242 is 1293994.

The greatest common factor of 464/314,6716/8242 = [GCF of 464,6716]/[LCM of 314,8242]= 4/1293994

Therefore, the GCF of 464/314,6716/8242 is 4/1293994.

Greatest Common Factor of 464,6716

To find the highest common factor of 464,6716, we have to find the factors of both numbers and list the highest common factor.

The factors of 464 are 1, 2, 4, 8, 16, 29, 58, 116, 232, 464

The factors of 6716 are 1, 2, 4, 23, 46, 73, 92, 146, 292, 1679, 3358, 6716

The HCF of 464,6716 is 4.

Lets's calculate GCF of 464,6716

Greatest Common Factor (GCF) of 464,6716 By Common Division

2	464, 6716
2	232, 3358
	116, 1679

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 464,6716 By Matching Biggest Common Factor Method

Now, list down the factors of 464

1,2,4,8,16,29,58,116,232,464

Now, list down the factors of 6716

1,2,4,23,46,73,92,146,292,1679,3358,6716

Greatest Common Factor

We found the factors 464,6716 . The biggest common factor number is the GCF number.
So the greatest common factor 464,6716 is 4.

Lets's calculate LCM of 314,8242

Lowest Common Multiple of 314,8242 using Common Division

2	314, 8242
	157, 4121

∴ So the LCM of the given numbers is 2 x 157 x 4121 = 1293994

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/1293994

Therefore, the GCF of Fractions 464/314,6716/8242 is 4/1293994

Least Common Multiple of 314,8242 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 314,8242 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(314,8242) = 2

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

GCF(314,8242) x common factors =2 x 1 = 2

LCM(314,8242) = ( 314 × 8242 ) / 2

LCM(314,8242) = 2587988 / 2

LCM(314,8242) = 1293994

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FAQs on GCF of Fractions of 464/314, 6716/8242

1. What is the HCF of 464,6716?

The HCF of 464,6716 is 4

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 464/314, 6716/8242?

Answer: GCF of Numerators as per given numbers 464/314, 6716/8242 is

GCF of Numerators i.e. for 464,6716 is 4

LCM of denominators i.e. for 314,8242 is 1293994.

Thus, GCF of Fractions is 4/1293994.Finally, GCF of Fractions for 464/314, 6716/8242 is 4/1293994.