How to Find GCF of 53/221, 37/689, 810/349?

GCF of 53/221, 37/689, 810/349

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 53/221, 37/689, 810/349 i.e 1/4087837 easily. The following is the detailed procedure to determine the greatest common factor of fractions 53/221, 37/689, 810/349.

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 53/221,37/689,810/349?

Given fractions are 53/221,37/689,810/349

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 53/221,37/689,810/349, numerators are 53,37,810

Denominators are 221,689,349

The GCF of 53,37,810 is 1 .

LCM of 221,689,349 is 4087837.

The greatest common factor of 53/221,37/689,810/349 = [GCF of 53,37,810]/[LCM of 221,689,349]= 1/4087837

Therefore, the GCF of 53/221,37/689,810/349 is 1/4087837.

Greatest Common Factor of 53,37,810

To find the highest common factor of 53,37,810, we have to find the factors of both numbers and list the highest common factor.

The factors of 53 are 1, 53

The factors of 37 are 1, 37

The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810

The HCF of 53,37,810 is 1.

Lets's calculate GCF of 53,37,810

Greatest Common Factor (GCF) of 53,37,810 By Common Division

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

Greatest Common Factor of 53,37,810 By Matching Biggest Common Factor Method

Now, list down the factors of 53

1,53

Now, list down the factors of 37

1,37

Now, list down the factors of 810

1,2,3,5,6,9,10,15,18,27,30,45,54,81,90,135,162,270,405,810

Greatest Common Factor

We found the factors 53,37,810 . The biggest common factor number is the GCF number.
So the greatest common factor 53,37,810 is 1.

Lets's calculate LCM of 221,689,349

Lowest Common Multiple of 221,689,349 using Common Division

13	221, 689, 349
	17, 53, 349

∴ So the LCM of the given numbers is 13 x 17 x 53 x 349 = 4087837

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4087837

Therefore, the GCF of Fractions 53/221,37/689,810/349 is 1/4087837

Least Common Multiple of 221,689,349 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 221,689,349 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(221,689,349) = 1

common factors(in case of two or more numbers have common factors) = 13

GCF(221,689,349) x common factors =1 x 13 = 13

LCM(221,689,349) = ( 221 × 689 × 349 ) / 13

LCM(221,689,349) = 53141881 / 13

LCM(221,689,349) = 4087837

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 53/221, 37/689, 810/349

1. What is the HCF of 53,37,810?

The HCF of 53,37,810 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 53/221, 37/689, 810/349?

Answer: GCF of Numerators as per given numbers 53/221, 37/689, 810/349 is

GCF of Numerators i.e. for 53,37,810 is 1

LCM of denominators i.e. for 221,689,349 is 4087837.

Thus, GCF of Fractions is 1/4087837.Finally, GCF of Fractions for 53/221, 37/689, 810/349 is 1/4087837.