How to Find GCF of 523/273, 8706/689?

GCF of 523/273, 8706/689

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 523/273, 8706/689 i.e 1/14469 easily. The following is the detailed procedure to determine the greatest common factor of fractions 523/273, 8706/689.

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 523/273,8706/689?

Given fractions are 523/273,8706/689

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 523/273,8706/689, numerators are 523,8706

Denominators are 273,689

The GCF of 523,8706 is 1 .

LCM of 273,689 is 14469.

The greatest common factor of 523/273,8706/689 = [GCF of 523,8706]/[LCM of 273,689]= 1/14469

Therefore, the GCF of 523/273,8706/689 is 1/14469.

Greatest Common Factor of 523,8706

To find the highest common factor of 523,8706, we have to find the factors of both numbers and list the highest common factor.

The factors of 523 are 1, 523

The factors of 8706 are 1, 2, 3, 6, 1451, 2902, 4353, 8706

The HCF of 523,8706 is 1.

Lets's calculate GCF of 523,8706

Greatest Common Factor (GCF) of 523,8706 By Common Division

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

Greatest Common Factor of 523,8706 By Matching Biggest Common Factor Method

Now, list down the factors of 523

1,523

Now, list down the factors of 8706

1,2,3,6,1451,2902,4353,8706

Greatest Common Factor

We found the factors 523,8706 . The biggest common factor number is the GCF number.
So the greatest common factor 523,8706 is 1.

Lets's calculate LCM of 273,689

Lowest Common Multiple of 273,689 using Common Division

13	273, 689
	21, 53

∴ So the LCM of the given numbers is 13 x 21 x 53 = 14469

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/14469

Therefore, the GCF of Fractions 523/273,8706/689 is 1/14469

Least Common Multiple of 273,689 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 273,689 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(273,689) = 13

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

GCF(273,689) x common factors =13 x 1 = 13

LCM(273,689) = ( 273 × 689 ) / 13

LCM(273,689) = 188097 / 13

LCM(273,689) = 14469

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FAQs on GCF of Fractions of 523/273, 8706/689

1. What is the HCF of 523,8706?

The HCF of 523,8706 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 523/273, 8706/689?

Answer: GCF of Numerators as per given numbers 523/273, 8706/689 is

GCF of Numerators i.e. for 523,8706 is 1

LCM of denominators i.e. for 273,689 is 14469.

Thus, GCF of Fractions is 1/14469.Finally, GCF of Fractions for 523/273, 8706/689 is 1/14469.