How to Find GCF of 569/676, 1146/208?

GCF of 569/676, 1146/208

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 569/676, 1146/208 i.e 1/2704 easily. The following is the detailed procedure to determine the greatest common factor of fractions 569/676, 1146/208.

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 569/676,1146/208?

Given fractions are 569/676,1146/208

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 569/676,1146/208, numerators are 569,1146

Denominators are 676,208

The GCF of 569,1146 is 1 .

LCM of 676,208 is 2704.

The greatest common factor of 569/676,1146/208 = [GCF of 569,1146]/[LCM of 676,208]= 1/2704

Therefore, the GCF of 569/676,1146/208 is 1/2704.

Greatest Common Factor of 569,1146

To find the highest common factor of 569,1146, we have to find the factors of both numbers and list the highest common factor.

The factors of 569 are 1, 569

The factors of 1146 are 1, 2, 3, 6, 191, 382, 573, 1146

The HCF of 569,1146 is 1.

Lets's calculate GCF of 569,1146

Greatest Common Factor (GCF) of 569,1146 By Common Division

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

Greatest Common Factor of 569,1146 By Matching Biggest Common Factor Method

Now, list down the factors of 569

1,569

Now, list down the factors of 1146

1,2,3,6,191,382,573,1146

Greatest Common Factor

We found the factors 569,1146 . The biggest common factor number is the GCF number.
So the greatest common factor 569,1146 is 1.

Lets's calculate LCM of 676,208

Lowest Common Multiple of 676,208 using Common Division

2	676, 208
2	338, 104
13	169, 52
	13, 4

∴ So the LCM of the given numbers is 2 x 2 x 13 x 13 x 4 = 2704

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2704

Therefore, the GCF of Fractions 569/676,1146/208 is 1/2704

Least Common Multiple of 676,208 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 676,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(676,208) = 52

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

GCF(676,208) x common factors =52 x 1 = 52

LCM(676,208) = ( 676 × 208 ) / 52

LCM(676,208) = 140608 / 52

LCM(676,208) = 2704

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FAQs on GCF of Fractions of 569/676, 1146/208

1. What is the HCF of 569,1146?

The HCF of 569,1146 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 569/676, 1146/208?

Answer: GCF of Numerators as per given numbers 569/676, 1146/208 is

GCF of Numerators i.e. for 569,1146 is 1

LCM of denominators i.e. for 676,208 is 2704.

Thus, GCF of Fractions is 1/2704.Finally, GCF of Fractions for 569/676, 1146/208 is 1/2704.