How to Find GCF of 9975/223, 7309/561?

GCF of 9975/223, 7309/561

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 9975/223, 7309/561 i.e 1/125103 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9975/223, 7309/561.

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 9975/223,7309/561?

Given fractions are 9975/223,7309/561

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 9975/223,7309/561, numerators are 9975,7309

Denominators are 223,561

The GCF of 9975,7309 is 1 .

LCM of 223,561 is 125103.

The greatest common factor of 9975/223,7309/561 = [GCF of 9975,7309]/[LCM of 223,561]= 1/125103

Therefore, the GCF of 9975/223,7309/561 is 1/125103.

Greatest Common Factor of 9975,7309

To find the highest common factor of 9975,7309, we have to find the factors of both numbers and list the highest common factor.

The factors of 9975 are 1, 3, 5, 7, 15, 19, 21, 25, 35, 57, 75, 95, 105, 133, 175, 285, 399, 475, 525, 665, 1425, 1995, 3325, 9975

The factors of 7309 are 1, 7309

The HCF of 9975,7309 is 1.

Lets's calculate GCF of 9975,7309

Greatest Common Factor (GCF) of 9975,7309 By Common Division

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

Greatest Common Factor of 9975,7309 By Matching Biggest Common Factor Method

Now, list down the factors of 9975

1,3,5,7,15,19,21,25,35,57,75,95,105,133,175,285,399,475,525,665,1425,1995,3325,9975

Now, list down the factors of 7309

1,7309

Greatest Common Factor

We found the factors 9975,7309 . The biggest common factor number is the GCF number.
So the greatest common factor 9975,7309 is 1.

Lets's calculate LCM of 223,561

Lowest Common Multiple of 223,561 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 125103

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/125103

Therefore, the GCF of Fractions 9975/223,7309/561 is 1/125103

Least Common Multiple of 223,561 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 223,561 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(223,561) = 1

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

GCF(223,561) x common factors =1 x 1 = 1

LCM(223,561) = ( 223 × 561 ) / 1

LCM(223,561) = 125103 / 1

LCM(223,561) = 125103

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 9975/223, 7309/561

1. What is the HCF of 9975,7309?

The HCF of 9975,7309 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 9975/223, 7309/561?

Answer: GCF of Numerators as per given numbers 9975/223, 7309/561 is

GCF of Numerators i.e. for 9975,7309 is 1

LCM of denominators i.e. for 223,561 is 125103.

Thus, GCF of Fractions is 1/125103.Finally, GCF of Fractions for 9975/223, 7309/561 is 1/125103.