How to Find GCF of 410/722, 3870/713?

GCF of 410/722, 3870/713

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 410/722, 3870/713 i.e 10/514786 easily. The following is the detailed procedure to determine the greatest common factor of fractions 410/722, 3870/713.

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 410/722,3870/713?

Given fractions are 410/722,3870/713

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 410/722,3870/713, numerators are 410,3870

Denominators are 722,713

The GCF of 410,3870 is 10 .

LCM of 722,713 is 514786.

The greatest common factor of 410/722,3870/713 = [GCF of 410,3870]/[LCM of 722,713]= 10/514786

Therefore, the GCF of 410/722,3870/713 is 10/514786.

Greatest Common Factor of 410,3870

To find the highest common factor of 410,3870, we have to find the factors of both numbers and list the highest common factor.

The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410

The factors of 3870 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 43, 45, 86, 90, 129, 215, 258, 387, 430, 645, 774, 1290, 1935, 3870

The HCF of 410,3870 is 10.

Lets's calculate GCF of 410,3870

Greatest Common Factor (GCF) of 410,3870 By Common Division

2	410, 3870
5	205, 1935
	41, 387

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 410,3870 By Matching Biggest Common Factor Method

Now, list down the factors of 410

1,2,5,10,41,82,205,410

Now, list down the factors of 3870

1,2,3,5,6,9,10,15,18,30,43,45,86,90,129,215,258,387,430,645,774,1290,1935,3870

Greatest Common Factor

We found the factors 410,3870 . The biggest common factor number is the GCF number.
So the greatest common factor 410,3870 is 10.

Lets's calculate LCM of 722,713

Lowest Common Multiple of 722,713 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 514786

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/514786

Therefore, the GCF of Fractions 410/722,3870/713 is 10/514786

Least Common Multiple of 722,713 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 722,713 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(722,713) = 1

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

GCF(722,713) x common factors =1 x 1 = 1

LCM(722,713) = ( 722 × 713 ) / 1

LCM(722,713) = 514786 / 1

LCM(722,713) = 514786

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FAQs on GCF of Fractions of 410/722, 3870/713

1. What is the HCF of 410,3870?

The HCF of 410,3870 is 10

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 410/722, 3870/713?

Answer: GCF of Numerators as per given numbers 410/722, 3870/713 is

GCF of Numerators i.e. for 410,3870 is 10

LCM of denominators i.e. for 722,713 is 514786.

Thus, GCF of Fractions is 10/514786.Finally, GCF of Fractions for 410/722, 3870/713 is 10/514786.