How to Find GCF of 4746/289, 2286/2377?

GCF of 4746/289, 2286/2377

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 4746/289, 2286/2377 i.e 6/686953 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4746/289, 2286/2377.

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 4746/289,2286/2377?

Given fractions are 4746/289,2286/2377

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 4746/289,2286/2377, numerators are 4746,2286

Denominators are 289,2377

The GCF of 4746,2286 is 6 .

LCM of 289,2377 is 686953.

The greatest common factor of 4746/289,2286/2377 = [GCF of 4746,2286]/[LCM of 289,2377]= 6/686953

Therefore, the GCF of 4746/289,2286/2377 is 6/686953.

Greatest Common Factor of 4746,2286

To find the highest common factor of 4746,2286, we have to find the factors of both numbers and list the highest common factor.

The factors of 4746 are 1, 2, 3, 6, 7, 14, 21, 42, 113, 226, 339, 678, 791, 1582, 2373, 4746

The factors of 2286 are 1, 2, 3, 6, 9, 18, 127, 254, 381, 762, 1143, 2286

The HCF of 4746,2286 is 6.

Lets's calculate GCF of 4746,2286

Greatest Common Factor (GCF) of 4746,2286 By Common Division

2	4746, 2286
3	2373, 1143
	791, 381

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 4746,2286 By Matching Biggest Common Factor Method

Now, list down the factors of 4746

1,2,3,6,7,14,21,42,113,226,339,678,791,1582,2373,4746

Now, list down the factors of 2286

1,2,3,6,9,18,127,254,381,762,1143,2286

Greatest Common Factor

We found the factors 4746,2286 . The biggest common factor number is the GCF number.
So the greatest common factor 4746,2286 is 6.

Lets's calculate LCM of 289,2377

Lowest Common Multiple of 289,2377 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 686953

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/686953

Therefore, the GCF of Fractions 4746/289,2286/2377 is 6/686953

Least Common Multiple of 289,2377 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 289,2377 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(289,2377) = 1

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

GCF(289,2377) x common factors =1 x 1 = 1

LCM(289,2377) = ( 289 × 2377 ) / 1

LCM(289,2377) = 686953 / 1

LCM(289,2377) = 686953

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 4746/289, 2286/2377

1. What is the HCF of 4746,2286?

The HCF of 4746,2286 is 6

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 4746/289, 2286/2377?

Answer: GCF of Numerators as per given numbers 4746/289, 2286/2377 is

GCF of Numerators i.e. for 4746,2286 is 6

LCM of denominators i.e. for 289,2377 is 686953.

Thus, GCF of Fractions is 6/686953.Finally, GCF of Fractions for 4746/289, 2286/2377 is 6/686953.