How to Find GCF of 3414/204, 6308/7802?

GCF of 3414/204, 6308/7802

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 3414/204, 6308/7802 i.e 2/795804 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3414/204, 6308/7802.

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 3414/204,6308/7802?

Given fractions are 3414/204,6308/7802

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 3414/204,6308/7802, numerators are 3414,6308

Denominators are 204,7802

The GCF of 3414,6308 is 2 .

LCM of 204,7802 is 795804.

The greatest common factor of 3414/204,6308/7802 = [GCF of 3414,6308]/[LCM of 204,7802]= 2/795804

Therefore, the GCF of 3414/204,6308/7802 is 2/795804.

Greatest Common Factor of 3414,6308

To find the highest common factor of 3414,6308, we have to find the factors of both numbers and list the highest common factor.

The factors of 3414 are 1, 2, 3, 6, 569, 1138, 1707, 3414

The factors of 6308 are 1, 2, 4, 19, 38, 76, 83, 166, 332, 1577, 3154, 6308

The HCF of 3414,6308 is 2.

Lets's calculate GCF of 3414,6308

Greatest Common Factor (GCF) of 3414,6308 By Common Division

2	3414, 6308
	1707, 3154

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

Greatest Common Factor of 3414,6308 By Matching Biggest Common Factor Method

Now, list down the factors of 3414

1,2,3,6,569,1138,1707,3414

Now, list down the factors of 6308

1,2,4,19,38,76,83,166,332,1577,3154,6308

Greatest Common Factor

We found the factors 3414,6308 . The biggest common factor number is the GCF number.
So the greatest common factor 3414,6308 is 2.

Lets's calculate LCM of 204,7802

Lowest Common Multiple of 204,7802 using Common Division

2	204, 7802
	102, 3901

∴ So the LCM of the given numbers is 2 x 102 x 3901 = 795804

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/795804

Therefore, the GCF of Fractions 3414/204,6308/7802 is 2/795804

Least Common Multiple of 204,7802 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 204,7802 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(204,7802) = 2

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

GCF(204,7802) x common factors =2 x 1 = 2

LCM(204,7802) = ( 204 × 7802 ) / 2

LCM(204,7802) = 1591608 / 2

LCM(204,7802) = 795804

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FAQs on GCF of Fractions of 3414/204, 6308/7802

1. What is the HCF of 3414,6308?

The HCF of 3414,6308 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 3414/204, 6308/7802?

Answer: GCF of Numerators as per given numbers 3414/204, 6308/7802 is

GCF of Numerators i.e. for 3414,6308 is 2

LCM of denominators i.e. for 204,7802 is 795804.

Thus, GCF of Fractions is 2/795804.Finally, GCF of Fractions for 3414/204, 6308/7802 is 2/795804.