How to Find GCF of 814/612, 6400/350?

GCF of 814/612, 6400/350

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 814/612, 6400/350 i.e 2/107100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 814/612, 6400/350.

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 814/612,6400/350?

Given fractions are 814/612,6400/350

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 814/612,6400/350, numerators are 814,6400

Denominators are 612,350

The GCF of 814,6400 is 2 .

LCM of 612,350 is 107100.

The greatest common factor of 814/612,6400/350 = [GCF of 814,6400]/[LCM of 612,350]= 2/107100

Therefore, the GCF of 814/612,6400/350 is 2/107100.

Greatest Common Factor of 814,6400

To find the highest common factor of 814,6400, we have to find the factors of both numbers and list the highest common factor.

The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814

The factors of 6400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 640, 800, 1280, 1600, 3200, 6400

The HCF of 814,6400 is 2.

Lets's calculate GCF of 814,6400

Greatest Common Factor (GCF) of 814,6400 By Common Division

2	814, 6400
	407, 3200

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

Greatest Common Factor of 814,6400 By Matching Biggest Common Factor Method

Now, list down the factors of 814

1,2,11,22,37,74,407,814

Now, list down the factors of 6400

1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,128,160,200,256,320,400,640,800,1280,1600,3200,6400

Greatest Common Factor

We found the factors 814,6400 . The biggest common factor number is the GCF number.
So the greatest common factor 814,6400 is 2.

Lets's calculate LCM of 612,350

Lowest Common Multiple of 612,350 using Common Division

2	612, 350
	306, 175

∴ So the LCM of the given numbers is 2 x 306 x 175 = 107100

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/107100

Therefore, the GCF of Fractions 814/612,6400/350 is 2/107100

Least Common Multiple of 612,350 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 612,350 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(612,350) = 2

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

GCF(612,350) x common factors =2 x 1 = 2

LCM(612,350) = ( 612 × 350 ) / 2

LCM(612,350) = 214200 / 2

LCM(612,350) = 107100

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FAQs on GCF of Fractions of 814/612, 6400/350

1. What is the HCF of 814,6400?

The HCF of 814,6400 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 814/612, 6400/350?

Answer: GCF of Numerators as per given numbers 814/612, 6400/350 is

GCF of Numerators i.e. for 814,6400 is 2

LCM of denominators i.e. for 612,350 is 107100.

Thus, GCF of Fractions is 2/107100.Finally, GCF of Fractions for 814/612, 6400/350 is 2/107100.