How to Find GCF of 7422/728, 7471/2080?

GCF of 7422/728, 7471/2080

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 7422/728, 7471/2080 i.e 1/14560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7422/728, 7471/2080.

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 7422/728,7471/2080?

Given fractions are 7422/728,7471/2080

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 7422/728,7471/2080, numerators are 7422,7471

Denominators are 728,2080

The GCF of 7422,7471 is 1 .

LCM of 728,2080 is 14560.

The greatest common factor of 7422/728,7471/2080 = [GCF of 7422,7471]/[LCM of 728,2080]= 1/14560

Therefore, the GCF of 7422/728,7471/2080 is 1/14560.

Greatest Common Factor of 7422,7471

To find the highest common factor of 7422,7471, we have to find the factors of both numbers and list the highest common factor.

The factors of 7422 are 1, 2, 3, 6, 1237, 2474, 3711, 7422

The factors of 7471 are 1, 31, 241, 7471

The HCF of 7422,7471 is 1.

Lets's calculate GCF of 7422,7471

Greatest Common Factor (GCF) of 7422,7471 By Common Division

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

Greatest Common Factor of 7422,7471 By Matching Biggest Common Factor Method

Now, list down the factors of 7422

1,2,3,6,1237,2474,3711,7422

Now, list down the factors of 7471

1,31,241,7471

Greatest Common Factor

We found the factors 7422,7471 . The biggest common factor number is the GCF number.
So the greatest common factor 7422,7471 is 1.

Lets's calculate LCM of 728,2080

Lowest Common Multiple of 728,2080 using Common Division

2	728, 2080
2	364, 1040
2	182, 520
13	91, 260
	7, 20

∴ So the LCM of the given numbers is 2 x 2 x 2 x 13 x 7 x 20 = 14560

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/14560

Therefore, the GCF of Fractions 7422/728,7471/2080 is 1/14560

Least Common Multiple of 728,2080 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 728,2080 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(728,2080) = 104

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

GCF(728,2080) x common factors =104 x 1 = 104

LCM(728,2080) = ( 728 × 2080 ) / 104

LCM(728,2080) = 1514240 / 104

LCM(728,2080) = 14560

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 7422/728, 7471/2080

1. What is the HCF of 7422,7471?

The HCF of 7422,7471 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 7422/728, 7471/2080?

Answer: GCF of Numerators as per given numbers 7422/728, 7471/2080 is

GCF of Numerators i.e. for 7422,7471 is 1

LCM of denominators i.e. for 728,2080 is 14560.

Thus, GCF of Fractions is 1/14560.Finally, GCF of Fractions for 7422/728, 7471/2080 is 1/14560.