How to Find GCF of 566/289, 7074/377?

GCF of 566/289, 7074/377

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 566/289, 7074/377 i.e 2/108953 easily. The following is the detailed procedure to determine the greatest common factor of fractions 566/289, 7074/377.

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 566/289,7074/377?

Given fractions are 566/289,7074/377

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 566/289,7074/377, numerators are 566,7074

Denominators are 289,377

The GCF of 566,7074 is 2 .

LCM of 289,377 is 108953.

The greatest common factor of 566/289,7074/377 = [GCF of 566,7074]/[LCM of 289,377]= 2/108953

Therefore, the GCF of 566/289,7074/377 is 2/108953.

Greatest Common Factor of 566,7074

To find the highest common factor of 566,7074, we have to find the factors of both numbers and list the highest common factor.

The factors of 566 are 1, 2, 283, 566

The factors of 7074 are 1, 2, 3, 6, 9, 18, 27, 54, 131, 262, 393, 786, 1179, 2358, 3537, 7074

The HCF of 566,7074 is 2.

Lets's calculate GCF of 566,7074

Greatest Common Factor (GCF) of 566,7074 By Common Division

2	566, 7074
	283, 3537

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 566,7074 By Matching Biggest Common Factor Method

Now, list down the factors of 566

1,2,283,566

Now, list down the factors of 7074

1,2,3,6,9,18,27,54,131,262,393,786,1179,2358,3537,7074

Greatest Common Factor

We found the factors 566,7074 . The biggest common factor number is the GCF number.
So the greatest common factor 566,7074 is 2.

Lets's calculate LCM of 289,377

Lowest Common Multiple of 289,377 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 108953

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/108953

Therefore, the GCF of Fractions 566/289,7074/377 is 2/108953

Least Common Multiple of 289,377 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 289,377 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(289,377) = 1

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

GCF(289,377) x common factors =1 x 1 = 1

LCM(289,377) = ( 289 × 377 ) / 1

LCM(289,377) = 108953 / 1

LCM(289,377) = 108953

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 566/289, 7074/377

1. What is the HCF of 566,7074?

The HCF of 566,7074 is 2

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 566/289, 7074/377?

Answer: GCF of Numerators as per given numbers 566/289, 7074/377 is

GCF of Numerators i.e. for 566,7074 is 2

LCM of denominators i.e. for 289,377 is 108953.

Thus, GCF of Fractions is 2/108953.Finally, GCF of Fractions for 566/289, 7074/377 is 2/108953.