How to Find GCF of 782/590, 5730/1429?

GCF of 782/590, 5730/1429

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 782/590, 5730/1429 i.e 2/843110 easily. The following is the detailed procedure to determine the greatest common factor of fractions 782/590, 5730/1429.

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 782/590,5730/1429?

Given fractions are 782/590,5730/1429

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 782/590,5730/1429, numerators are 782,5730

Denominators are 590,1429

The GCF of 782,5730 is 2 .

LCM of 590,1429 is 843110.

The greatest common factor of 782/590,5730/1429 = [GCF of 782,5730]/[LCM of 590,1429]= 2/843110

Therefore, the GCF of 782/590,5730/1429 is 2/843110.

Greatest Common Factor of 782,5730

To find the highest common factor of 782,5730, we have to find the factors of both numbers and list the highest common factor.

The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782

The factors of 5730 are 1, 2, 3, 5, 6, 10, 15, 30, 191, 382, 573, 955, 1146, 1910, 2865, 5730

The HCF of 782,5730 is 2.

Lets's calculate GCF of 782,5730

Greatest Common Factor (GCF) of 782,5730 By Common Division

2	782, 5730
	391, 2865

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

Greatest Common Factor of 782,5730 By Matching Biggest Common Factor Method

Now, list down the factors of 782

1,2,17,23,34,46,391,782

Now, list down the factors of 5730

1,2,3,5,6,10,15,30,191,382,573,955,1146,1910,2865,5730

Greatest Common Factor

We found the factors 782,5730 . The biggest common factor number is the GCF number.
So the greatest common factor 782,5730 is 2.

Lets's calculate LCM of 590,1429

Lowest Common Multiple of 590,1429 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 843110

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/843110

Therefore, the GCF of Fractions 782/590,5730/1429 is 2/843110

Least Common Multiple of 590,1429 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 590,1429 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(590,1429) = 1

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

GCF(590,1429) x common factors =1 x 1 = 1

LCM(590,1429) = ( 590 × 1429 ) / 1

LCM(590,1429) = 843110 / 1

LCM(590,1429) = 843110

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FAQs on GCF of Fractions of 782/590, 5730/1429

1. What is the HCF of 782,5730?

The HCF of 782,5730 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 782/590, 5730/1429?

Answer: GCF of Numerators as per given numbers 782/590, 5730/1429 is

GCF of Numerators i.e. for 782,5730 is 2

LCM of denominators i.e. for 590,1429 is 843110.

Thus, GCF of Fractions is 2/843110.Finally, GCF of Fractions for 782/590, 5730/1429 is 2/843110.