How to Find GCF of 582/460, 760/416?

GCF of 582/460, 760/416

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 582/460, 760/416 i.e 2/47840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 582/460, 760/416.

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 582/460,760/416?

Given fractions are 582/460,760/416

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 582/460,760/416, numerators are 582,760

Denominators are 460,416

The GCF of 582,760 is 2 .

LCM of 460,416 is 47840.

The greatest common factor of 582/460,760/416 = [GCF of 582,760]/[LCM of 460,416]= 2/47840

Therefore, the GCF of 582/460,760/416 is 2/47840.

Greatest Common Factor of 582,760

To find the highest common factor of 582,760, we have to find the factors of both numbers and list the highest common factor.

The factors of 582 are 1, 2, 3, 6, 97, 194, 291, 582

The factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760

The HCF of 582,760 is 2.

Lets's calculate GCF of 582,760

Greatest Common Factor (GCF) of 582,760 By Common Division

2	582, 760
	291, 380

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

Greatest Common Factor of 582,760 By Matching Biggest Common Factor Method

Now, list down the factors of 582

1,2,3,6,97,194,291,582

Now, list down the factors of 760

1,2,4,5,8,10,19,20,38,40,76,95,152,190,380,760

Greatest Common Factor

We found the factors 582,760 . The biggest common factor number is the GCF number.
So the greatest common factor 582,760 is 2.

Lets's calculate LCM of 460,416

Lowest Common Multiple of 460,416 using Common Division

2	460, 416
2	230, 208
	115, 104

∴ So the LCM of the given numbers is 2 x 2 x 115 x 104 = 47840

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/47840

Therefore, the GCF of Fractions 582/460,760/416 is 2/47840

Least Common Multiple of 460,416 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 460,416 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(460,416) = 4

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

GCF(460,416) x common factors =4 x 1 = 4

LCM(460,416) = ( 460 × 416 ) / 4

LCM(460,416) = 191360 / 4

LCM(460,416) = 47840

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FAQs on GCF of Fractions of 582/460, 760/416

1. What is the HCF of 582,760?

The HCF of 582,760 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 582/460, 760/416?

Answer: GCF of Numerators as per given numbers 582/460, 760/416 is

GCF of Numerators i.e. for 582,760 is 2

LCM of denominators i.e. for 460,416 is 47840.

Thus, GCF of Fractions is 2/47840.Finally, GCF of Fractions for 582/460, 760/416 is 2/47840.