How to Find GCF of 3638/314, 7789/6758?

GCF of 3638/314, 7789/6758

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 3638/314, 7789/6758 i.e 1/1061006 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3638/314, 7789/6758.

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 3638/314,7789/6758?

Given fractions are 3638/314,7789/6758

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 3638/314,7789/6758, numerators are 3638,7789

Denominators are 314,6758

The GCF of 3638,7789 is 1 .

LCM of 314,6758 is 1061006.

The greatest common factor of 3638/314,7789/6758 = [GCF of 3638,7789]/[LCM of 314,6758]= 1/1061006

Therefore, the GCF of 3638/314,7789/6758 is 1/1061006.

Greatest Common Factor of 3638,7789

To find the highest common factor of 3638,7789, we have to find the factors of both numbers and list the highest common factor.

The factors of 3638 are 1, 2, 17, 34, 107, 214, 1819, 3638

The factors of 7789 are 1, 7789

The HCF of 3638,7789 is 1.

Lets's calculate GCF of 3638,7789

Greatest Common Factor (GCF) of 3638,7789 By Common Division

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

Greatest Common Factor of 3638,7789 By Matching Biggest Common Factor Method

Now, list down the factors of 3638

1,2,17,34,107,214,1819,3638

Now, list down the factors of 7789

1,7789

Greatest Common Factor

We found the factors 3638,7789 . The biggest common factor number is the GCF number.
So the greatest common factor 3638,7789 is 1.

Lets's calculate LCM of 314,6758

Lowest Common Multiple of 314,6758 using Common Division

2	314, 6758
	157, 3379

∴ So the LCM of the given numbers is 2 x 157 x 3379 = 1061006

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1061006

Therefore, the GCF of Fractions 3638/314,7789/6758 is 1/1061006

Least Common Multiple of 314,6758 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 314,6758 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(314,6758) = 2

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

GCF(314,6758) x common factors =2 x 1 = 2

LCM(314,6758) = ( 314 × 6758 ) / 2

LCM(314,6758) = 2122012 / 2

LCM(314,6758) = 1061006

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FAQs on GCF of Fractions of 3638/314, 7789/6758

1. What is the HCF of 3638,7789?

The HCF of 3638,7789 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 3638/314, 7789/6758?

Answer: GCF of Numerators as per given numbers 3638/314, 7789/6758 is

GCF of Numerators i.e. for 3638,7789 is 1

LCM of denominators i.e. for 314,6758 is 1061006.

Thus, GCF of Fractions is 1/1061006.Finally, GCF of Fractions for 3638/314, 7789/6758 is 1/1061006.