How to Find GCF of 3431/288, 6821/8136?

GCF of 3431/288, 6821/8136

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 3431/288, 6821/8136 i.e 1/32544 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3431/288, 6821/8136.

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 3431/288,6821/8136?

Given fractions are 3431/288,6821/8136

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 3431/288,6821/8136, numerators are 3431,6821

Denominators are 288,8136

The GCF of 3431,6821 is 1 .

LCM of 288,8136 is 32544.

The greatest common factor of 3431/288,6821/8136 = [GCF of 3431,6821]/[LCM of 288,8136]= 1/32544

Therefore, the GCF of 3431/288,6821/8136 is 1/32544.

Greatest Common Factor of 3431,6821

To find the highest common factor of 3431,6821, we have to find the factors of both numbers and list the highest common factor.

The factors of 3431 are 1, 47, 73, 3431

The factors of 6821 are 1, 19, 359, 6821

The HCF of 3431,6821 is 1.

Lets's calculate GCF of 3431,6821

Greatest Common Factor (GCF) of 3431,6821 By Common Division

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

Greatest Common Factor of 3431,6821 By Matching Biggest Common Factor Method

Now, list down the factors of 3431

1,47,73,3431

Now, list down the factors of 6821

1,19,359,6821

Greatest Common Factor

We found the factors 3431,6821 . The biggest common factor number is the GCF number.
So the greatest common factor 3431,6821 is 1.

Lets's calculate LCM of 288,8136

Lowest Common Multiple of 288,8136 using Common Division

2	288, 8136
2	144, 4068
2	72, 2034
3	36, 1017
3	12, 339
	4, 113

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 3 x 4 x 113 = 32544

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/32544

Therefore, the GCF of Fractions 3431/288,6821/8136 is 1/32544

Least Common Multiple of 288,8136 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 288,8136 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(288,8136) = 72

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

GCF(288,8136) x common factors =72 x 1 = 72

LCM(288,8136) = ( 288 × 8136 ) / 72

LCM(288,8136) = 2343168 / 72

LCM(288,8136) = 32544

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FAQs on GCF of Fractions of 3431/288, 6821/8136

1. What is the HCF of 3431,6821?

The HCF of 3431,6821 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 3431/288, 6821/8136?

Answer: GCF of Numerators as per given numbers 3431/288, 6821/8136 is

GCF of Numerators i.e. for 3431,6821 is 1

LCM of denominators i.e. for 288,8136 is 32544.

Thus, GCF of Fractions is 1/32544.Finally, GCF of Fractions for 3431/288, 6821/8136 is 1/32544.