How to Find GCF of 824/653, 5302/1731?

GCF of 824/653, 5302/1731

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 824/653, 5302/1731 i.e 2/1130343 easily. The following is the detailed procedure to determine the greatest common factor of fractions 824/653, 5302/1731.

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 824/653,5302/1731?

Given fractions are 824/653,5302/1731

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 824/653,5302/1731, numerators are 824,5302

Denominators are 653,1731

The GCF of 824,5302 is 2 .

LCM of 653,1731 is 1130343.

The greatest common factor of 824/653,5302/1731 = [GCF of 824,5302]/[LCM of 653,1731]= 2/1130343

Therefore, the GCF of 824/653,5302/1731 is 2/1130343.

Greatest Common Factor of 824,5302

To find the highest common factor of 824,5302, we have to find the factors of both numbers and list the highest common factor.

The factors of 824 are 1, 2, 4, 8, 103, 206, 412, 824

The factors of 5302 are 1, 2, 11, 22, 241, 482, 2651, 5302

The HCF of 824,5302 is 2.

Lets's calculate GCF of 824,5302

Greatest Common Factor (GCF) of 824,5302 By Common Division

2	824, 5302
	412, 2651

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

Greatest Common Factor of 824,5302 By Matching Biggest Common Factor Method

Now, list down the factors of 824

1,2,4,8,103,206,412,824

Now, list down the factors of 5302

1,2,11,22,241,482,2651,5302

Greatest Common Factor

We found the factors 824,5302 . The biggest common factor number is the GCF number.
So the greatest common factor 824,5302 is 2.

Lets's calculate LCM of 653,1731

Lowest Common Multiple of 653,1731 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1130343

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1130343

Therefore, the GCF of Fractions 824/653,5302/1731 is 2/1130343

Least Common Multiple of 653,1731 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 653,1731 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(653,1731) = 1

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

GCF(653,1731) x common factors =1 x 1 = 1

LCM(653,1731) = ( 653 × 1731 ) / 1

LCM(653,1731) = 1130343 / 1

LCM(653,1731) = 1130343

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 824/653, 5302/1731

1. What is the HCF of 824,5302?

The HCF of 824,5302 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 824/653, 5302/1731?

Answer: GCF of Numerators as per given numbers 824/653, 5302/1731 is

GCF of Numerators i.e. for 824,5302 is 2

LCM of denominators i.e. for 653,1731 is 1130343.

Thus, GCF of Fractions is 2/1130343.Finally, GCF of Fractions for 824/653, 5302/1731 is 2/1130343.