How to Find GCF of 741/161, 722/219?

GCF of 741/161, 722/219

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 741/161, 722/219 i.e 19/35259 easily. The following is the detailed procedure to determine the greatest common factor of fractions 741/161, 722/219.

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 741/161,722/219?

Given fractions are 741/161,722/219

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 741/161,722/219, numerators are 741,722

Denominators are 161,219

The GCF of 741,722 is 19 .

LCM of 161,219 is 35259.

The greatest common factor of 741/161,722/219 = [GCF of 741,722]/[LCM of 161,219]= 19/35259

Therefore, the GCF of 741/161,722/219 is 19/35259.

Greatest Common Factor of 741,722

To find the highest common factor of 741,722, we have to find the factors of both numbers and list the highest common factor.

The factors of 741 are 1, 3, 13, 19, 39, 57, 247, 741

The factors of 722 are 1, 2, 19, 38, 361, 722

The HCF of 741,722 is 19.

Lets's calculate GCF of 741,722

Greatest Common Factor (GCF) of 741,722 By Common Division

19	741, 722
	39, 38

∴ So the GCF of the given numbers is 19 = 19

Greatest Common Factor of 741,722 By Matching Biggest Common Factor Method

Now, list down the factors of 741

1,3,13,19,39,57,247,741

Now, list down the factors of 722

1,2,19,38,361,722

Greatest Common Factor

We found the factors 741,722 . The biggest common factor number is the GCF number.
So the greatest common factor 741,722 is 19.

Lets's calculate LCM of 161,219

Lowest Common Multiple of 161,219 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 35259

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/35259

Therefore, the GCF of Fractions 741/161,722/219 is 19/35259

Least Common Multiple of 161,219 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 161,219 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(161,219) = 1

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

GCF(161,219) x common factors =1 x 1 = 1

LCM(161,219) = ( 161 × 219 ) / 1

LCM(161,219) = 35259 / 1

LCM(161,219) = 35259

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FAQs on GCF of Fractions of 741/161, 722/219

1. What is the HCF of 741,722?

The HCF of 741,722 is 19

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 741/161, 722/219?

Answer: GCF of Numerators as per given numbers 741/161, 722/219 is

GCF of Numerators i.e. for 741,722 is 19

LCM of denominators i.e. for 161,219 is 35259.

Thus, GCF of Fractions is 19/35259.Finally, GCF of Fractions for 741/161, 722/219 is 19/35259.