How to Find GCF of 8004/342, 6305/4114?

GCF of 8004/342, 6305/4114

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 8004/342, 6305/4114 i.e 1/703494 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8004/342, 6305/4114.

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 8004/342,6305/4114?

Given fractions are 8004/342,6305/4114

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 8004/342,6305/4114, numerators are 8004,6305

Denominators are 342,4114

The GCF of 8004,6305 is 1 .

LCM of 342,4114 is 703494.

The greatest common factor of 8004/342,6305/4114 = [GCF of 8004,6305]/[LCM of 342,4114]= 1/703494

Therefore, the GCF of 8004/342,6305/4114 is 1/703494.

Greatest Common Factor of 8004,6305

To find the highest common factor of 8004,6305, we have to find the factors of both numbers and list the highest common factor.

The factors of 8004 are 1, 2, 3, 4, 6, 12, 23, 29, 46, 58, 69, 87, 92, 116, 138, 174, 276, 348, 667, 1334, 2001, 2668, 4002, 8004

The factors of 6305 are 1, 5, 13, 65, 97, 485, 1261, 6305

The HCF of 8004,6305 is 1.

Lets's calculate GCF of 8004,6305

Greatest Common Factor (GCF) of 8004,6305 By Common Division

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

Greatest Common Factor of 8004,6305 By Matching Biggest Common Factor Method

Now, list down the factors of 8004

1,2,3,4,6,12,23,29,46,58,69,87,92,116,138,174,276,348,667,1334,2001,2668,4002,8004

Now, list down the factors of 6305

1,5,13,65,97,485,1261,6305

Greatest Common Factor

We found the factors 8004,6305 . The biggest common factor number is the GCF number.
So the greatest common factor 8004,6305 is 1.

Lets's calculate LCM of 342,4114

Lowest Common Multiple of 342,4114 using Common Division

2	342, 4114
	171, 2057

∴ So the LCM of the given numbers is 2 x 171 x 2057 = 703494

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/703494

Therefore, the GCF of Fractions 8004/342,6305/4114 is 1/703494

Least Common Multiple of 342,4114 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 342,4114 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(342,4114) = 2

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

GCF(342,4114) x common factors =2 x 1 = 2

LCM(342,4114) = ( 342 × 4114 ) / 2

LCM(342,4114) = 1406988 / 2

LCM(342,4114) = 703494

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FAQs on GCF of Fractions of 8004/342, 6305/4114

1. What is the HCF of 8004,6305?

The HCF of 8004,6305 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 8004/342, 6305/4114?

Answer: GCF of Numerators as per given numbers 8004/342, 6305/4114 is

GCF of Numerators i.e. for 8004,6305 is 1

LCM of denominators i.e. for 342,4114 is 703494.

Thus, GCF of Fractions is 1/703494.Finally, GCF of Fractions for 8004/342, 6305/4114 is 1/703494.