How to Find GCF of 7330/584, 7882/1460?

GCF of 7330/584, 7882/1460

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 7330/584, 7882/1460 i.e 2/2920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7330/584, 7882/1460.

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 7330/584,7882/1460?

Given fractions are 7330/584,7882/1460

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 7330/584,7882/1460, numerators are 7330,7882

Denominators are 584,1460

The GCF of 7330,7882 is 2 .

LCM of 584,1460 is 2920.

The greatest common factor of 7330/584,7882/1460 = [GCF of 7330,7882]/[LCM of 584,1460]= 2/2920

Therefore, the GCF of 7330/584,7882/1460 is 2/2920.

Greatest Common Factor of 7330,7882

To find the highest common factor of 7330,7882, we have to find the factors of both numbers and list the highest common factor.

The factors of 7330 are 1, 2, 5, 10, 733, 1466, 3665, 7330

The factors of 7882 are 1, 2, 7, 14, 563, 1126, 3941, 7882

The HCF of 7330,7882 is 2.

Lets's calculate GCF of 7330,7882

Greatest Common Factor (GCF) of 7330,7882 By Common Division

2	7330, 7882
	3665, 3941

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 7330,7882 By Matching Biggest Common Factor Method

Now, list down the factors of 7330

1,2,5,10,733,1466,3665,7330

Now, list down the factors of 7882

1,2,7,14,563,1126,3941,7882

Greatest Common Factor

We found the factors 7330,7882 . The biggest common factor number is the GCF number.
So the greatest common factor 7330,7882 is 2.

Lets's calculate LCM of 584,1460

Lowest Common Multiple of 584,1460 using Common Division

2	584, 1460
2	292, 730
73	146, 365
	2, 5

∴ So the LCM of the given numbers is 2 x 2 x 73 x 2 x 5 = 2920

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2920

Therefore, the GCF of Fractions 7330/584,7882/1460 is 2/2920

Least Common Multiple of 584,1460 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 584,1460 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(584,1460) = 292

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

GCF(584,1460) x common factors =292 x 1 = 292

LCM(584,1460) = ( 584 × 1460 ) / 292

LCM(584,1460) = 852640 / 292

LCM(584,1460) = 2920

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 7330/584, 7882/1460

1. What is the HCF of 7330,7882?

The HCF of 7330,7882 is 2

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 7330/584, 7882/1460?

Answer: GCF of Numerators as per given numbers 7330/584, 7882/1460 is

GCF of Numerators i.e. for 7330,7882 is 2

LCM of denominators i.e. for 584,1460 is 2920.

Thus, GCF of Fractions is 2/2920.Finally, GCF of Fractions for 7330/584, 7882/1460 is 2/2920.