How to Find GCF of 7678/289, 6599/6802?

GCF of 7678/289, 6599/6802

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 7678/289, 6599/6802 i.e 1/1965778 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7678/289, 6599/6802.

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 7678/289,6599/6802?

Given fractions are 7678/289,6599/6802

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 7678/289,6599/6802, numerators are 7678,6599

Denominators are 289,6802

The GCF of 7678,6599 is 1 .

LCM of 289,6802 is 1965778.

The greatest common factor of 7678/289,6599/6802 = [GCF of 7678,6599]/[LCM of 289,6802]= 1/1965778

Therefore, the GCF of 7678/289,6599/6802 is 1/1965778.

Greatest Common Factor of 7678,6599

To find the highest common factor of 7678,6599, we have to find the factors of both numbers and list the highest common factor.

The factors of 7678 are 1, 2, 11, 22, 349, 698, 3839, 7678

The factors of 6599 are 1, 6599

The HCF of 7678,6599 is 1.

Lets's calculate GCF of 7678,6599

Greatest Common Factor (GCF) of 7678,6599 By Common Division

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

Greatest Common Factor of 7678,6599 By Matching Biggest Common Factor Method

Now, list down the factors of 7678

1,2,11,22,349,698,3839,7678

Now, list down the factors of 6599

1,6599

Greatest Common Factor

We found the factors 7678,6599 . The biggest common factor number is the GCF number.
So the greatest common factor 7678,6599 is 1.

Lets's calculate LCM of 289,6802

Lowest Common Multiple of 289,6802 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1965778

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1965778

Therefore, the GCF of Fractions 7678/289,6599/6802 is 1/1965778

Least Common Multiple of 289,6802 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 289,6802 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(289,6802) = 1

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

GCF(289,6802) x common factors =1 x 1 = 1

LCM(289,6802) = ( 289 × 6802 ) / 1

LCM(289,6802) = 1965778 / 1

LCM(289,6802) = 1965778

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FAQs on GCF of Fractions of 7678/289, 6599/6802

1. What is the HCF of 7678,6599?

The HCF of 7678,6599 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 7678/289, 6599/6802?

Answer: GCF of Numerators as per given numbers 7678/289, 6599/6802 is

GCF of Numerators i.e. for 7678,6599 is 1

LCM of denominators i.e. for 289,6802 is 1965778.

Thus, GCF of Fractions is 1/1965778.Finally, GCF of Fractions for 7678/289, 6599/6802 is 1/1965778.