How to Find GCF of 5789/314, 2106/9944?

GCF of 5789/314, 2106/9944

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 5789/314, 2106/9944 i.e 1/1561208 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5789/314, 2106/9944.

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 5789/314,2106/9944?

Given fractions are 5789/314,2106/9944

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 5789/314,2106/9944, numerators are 5789,2106

Denominators are 314,9944

The GCF of 5789,2106 is 1 .

LCM of 314,9944 is 1561208.

The greatest common factor of 5789/314,2106/9944 = [GCF of 5789,2106]/[LCM of 314,9944]= 1/1561208

Therefore, the GCF of 5789/314,2106/9944 is 1/1561208.

Greatest Common Factor of 5789,2106

To find the highest common factor of 5789,2106, we have to find the factors of both numbers and list the highest common factor.

The factors of 5789 are 1, 7, 827, 5789

The factors of 2106 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 81, 117, 162, 234, 351, 702, 1053, 2106

The HCF of 5789,2106 is 1.

Lets's calculate GCF of 5789,2106

Greatest Common Factor (GCF) of 5789,2106 By Common Division

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

Greatest Common Factor of 5789,2106 By Matching Biggest Common Factor Method

Now, list down the factors of 5789

1,7,827,5789

Now, list down the factors of 2106

1,2,3,6,9,13,18,26,27,39,54,78,81,117,162,234,351,702,1053,2106

Greatest Common Factor

We found the factors 5789,2106 . The biggest common factor number is the GCF number.
So the greatest common factor 5789,2106 is 1.

Lets's calculate LCM of 314,9944

Lowest Common Multiple of 314,9944 using Common Division

2	314, 9944
	157, 4972

∴ So the LCM of the given numbers is 2 x 157 x 4972 = 1561208

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1561208

Therefore, the GCF of Fractions 5789/314,2106/9944 is 1/1561208

Least Common Multiple of 314,9944 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 314,9944 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(314,9944) = 2

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

GCF(314,9944) x common factors =2 x 1 = 2

LCM(314,9944) = ( 314 × 9944 ) / 2

LCM(314,9944) = 3122416 / 2

LCM(314,9944) = 1561208

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FAQs on GCF of Fractions of 5789/314, 2106/9944

1. What is the HCF of 5789,2106?

The HCF of 5789,2106 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 5789/314, 2106/9944?

Answer: GCF of Numerators as per given numbers 5789/314, 2106/9944 is

GCF of Numerators i.e. for 5789,2106 is 1

LCM of denominators i.e. for 314,9944 is 1561208.

Thus, GCF of Fractions is 1/1561208.Finally, GCF of Fractions for 5789/314, 2106/9944 is 1/1561208.