How to Find GCF of 7261/322, 2223/7758?

GCF of 7261/322, 2223/7758

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 7261/322, 2223/7758 i.e 1/1249038 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7261/322, 2223/7758.

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 7261/322,2223/7758?

Given fractions are 7261/322,2223/7758

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 7261/322,2223/7758, numerators are 7261,2223

Denominators are 322,7758

The GCF of 7261,2223 is 1 .

LCM of 322,7758 is 1249038.

The greatest common factor of 7261/322,2223/7758 = [GCF of 7261,2223]/[LCM of 322,7758]= 1/1249038

Therefore, the GCF of 7261/322,2223/7758 is 1/1249038.

Greatest Common Factor of 7261,2223

To find the highest common factor of 7261,2223, we have to find the factors of both numbers and list the highest common factor.

The factors of 7261 are 1, 53, 137, 7261

The factors of 2223 are 1, 3, 9, 13, 19, 39, 57, 117, 171, 247, 741, 2223

The HCF of 7261,2223 is 1.

Lets's calculate GCF of 7261,2223

Greatest Common Factor (GCF) of 7261,2223 By Common Division

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

Greatest Common Factor of 7261,2223 By Matching Biggest Common Factor Method

Now, list down the factors of 7261

1,53,137,7261

Now, list down the factors of 2223

1,3,9,13,19,39,57,117,171,247,741,2223

Greatest Common Factor

We found the factors 7261,2223 . The biggest common factor number is the GCF number.
So the greatest common factor 7261,2223 is 1.

Lets's calculate LCM of 322,7758

Lowest Common Multiple of 322,7758 using Common Division

2	322, 7758
	161, 3879

∴ So the LCM of the given numbers is 2 x 161 x 3879 = 1249038

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1249038

Therefore, the GCF of Fractions 7261/322,2223/7758 is 1/1249038

Least Common Multiple of 322,7758 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 322,7758 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(322,7758) = 2

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

GCF(322,7758) x common factors =2 x 1 = 2

LCM(322,7758) = ( 322 × 7758 ) / 2

LCM(322,7758) = 2498076 / 2

LCM(322,7758) = 1249038

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FAQs on GCF of Fractions of 7261/322, 2223/7758

1. What is the HCF of 7261,2223?

The HCF of 7261,2223 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 7261/322, 2223/7758?

Answer: GCF of Numerators as per given numbers 7261/322, 2223/7758 is

GCF of Numerators i.e. for 7261,2223 is 1

LCM of denominators i.e. for 322,7758 is 1249038.

Thus, GCF of Fractions is 1/1249038.Finally, GCF of Fractions for 7261/322, 2223/7758 is 1/1249038.