How to Find GCF of 800/613, 7684/622?

GCF of 800/613, 7684/622

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 800/613, 7684/622 i.e 4/381286 easily. The following is the detailed procedure to determine the greatest common factor of fractions 800/613, 7684/622.

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 800/613,7684/622?

Given fractions are 800/613,7684/622

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 800/613,7684/622, numerators are 800,7684

Denominators are 613,622

The GCF of 800,7684 is 4 .

LCM of 613,622 is 381286.

The greatest common factor of 800/613,7684/622 = [GCF of 800,7684]/[LCM of 613,622]= 4/381286

Therefore, the GCF of 800/613,7684/622 is 4/381286.

Greatest Common Factor of 800,7684

To find the highest common factor of 800,7684, we have to find the factors of both numbers and list the highest common factor.

The factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800

The factors of 7684 are 1, 2, 4, 17, 34, 68, 113, 226, 452, 1921, 3842, 7684

The HCF of 800,7684 is 4.

Lets's calculate GCF of 800,7684

Greatest Common Factor (GCF) of 800,7684 By Common Division

2	800, 7684
2	400, 3842
	200, 1921

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

Greatest Common Factor of 800,7684 By Matching Biggest Common Factor Method

Now, list down the factors of 800

1,2,4,5,8,10,16,20,25,32,40,50,80,100,160,200,400,800

Now, list down the factors of 7684

1,2,4,17,34,68,113,226,452,1921,3842,7684

Greatest Common Factor

We found the factors 800,7684 . The biggest common factor number is the GCF number.
So the greatest common factor 800,7684 is 4.

Lets's calculate LCM of 613,622

Lowest Common Multiple of 613,622 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 381286

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/381286

Therefore, the GCF of Fractions 800/613,7684/622 is 4/381286

Least Common Multiple of 613,622 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 613,622 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(613,622) = 1

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

GCF(613,622) x common factors =1 x 1 = 1

LCM(613,622) = ( 613 × 622 ) / 1

LCM(613,622) = 381286 / 1

LCM(613,622) = 381286

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FAQs on GCF of Fractions of 800/613, 7684/622

1. What is the HCF of 800,7684?

The HCF of 800,7684 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 800/613, 7684/622?

Answer: GCF of Numerators as per given numbers 800/613, 7684/622 is

GCF of Numerators i.e. for 800,7684 is 4

LCM of denominators i.e. for 613,622 is 381286.

Thus, GCF of Fractions is 4/381286.Finally, GCF of Fractions for 800/613, 7684/622 is 4/381286.