How to Find GCF of 583/31, 825/7303?

GCF of 583/31, 825/7303

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 583/31, 825/7303 i.e 11/226393 easily. The following is the detailed procedure to determine the greatest common factor of fractions 583/31, 825/7303.

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 583/31,825/7303?

Given fractions are 583/31,825/7303

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 583/31,825/7303, numerators are 583,825

Denominators are 31,7303

The GCF of 583,825 is 11 .

LCM of 31,7303 is 226393.

The greatest common factor of 583/31,825/7303 = [GCF of 583,825]/[LCM of 31,7303]= 11/226393

Therefore, the GCF of 583/31,825/7303 is 11/226393.

Greatest Common Factor of 583,825

To find the highest common factor of 583,825, we have to find the factors of both numbers and list the highest common factor.

The factors of 583 are 1, 11, 53, 583

The factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825

The HCF of 583,825 is 11.

Lets's calculate GCF of 583,825

Greatest Common Factor (GCF) of 583,825 By Common Division

11	583, 825
	53, 75

∴ So the GCF of the given numbers is 11 = 11

Greatest Common Factor of 583,825 By Matching Biggest Common Factor Method

Now, list down the factors of 583

1,11,53,583

Now, list down the factors of 825

1,3,5,11,15,25,33,55,75,165,275,825

Greatest Common Factor

We found the factors 583,825 . The biggest common factor number is the GCF number.
So the greatest common factor 583,825 is 11.

Lets's calculate LCM of 31,7303

Lowest Common Multiple of 31,7303 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 226393

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/226393

Therefore, the GCF of Fractions 583/31,825/7303 is 11/226393

Least Common Multiple of 31,7303 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 31,7303 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,7303) = 1

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

GCF(31,7303) x common factors =1 x 1 = 1

LCM(31,7303) = ( 31 × 7303 ) / 1

LCM(31,7303) = 226393 / 1

LCM(31,7303) = 226393

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FAQs on GCF of Fractions of 583/31, 825/7303

1. What is the HCF of 583,825?

The HCF of 583,825 is 11

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 583/31, 825/7303?

Answer: GCF of Numerators as per given numbers 583/31, 825/7303 is

GCF of Numerators i.e. for 583,825 is 11

LCM of denominators i.e. for 31,7303 is 226393.

Thus, GCF of Fractions is 11/226393.Finally, GCF of Fractions for 583/31, 825/7303 is 11/226393.