How to Find GCF of 406/396, 870/513?

GCF of 406/396, 870/513

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 406/396, 870/513 i.e 58/22572 easily. The following is the detailed procedure to determine the greatest common factor of fractions 406/396, 870/513.

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 406/396,870/513?

Given fractions are 406/396,870/513

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 406/396,870/513, numerators are 406,870

Denominators are 396,513

The GCF of 406,870 is 58 .

LCM of 396,513 is 22572.

The greatest common factor of 406/396,870/513 = [GCF of 406,870]/[LCM of 396,513]= 58/22572

Therefore, the GCF of 406/396,870/513 is 58/22572.

Greatest Common Factor of 406,870

To find the highest common factor of 406,870, we have to find the factors of both numbers and list the highest common factor.

The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406

The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870

The HCF of 406,870 is 58.

Lets's calculate GCF of 406,870

Greatest Common Factor (GCF) of 406,870 By Common Division

2	406, 870
29	203, 435
	7, 15

∴ So the GCF of the given numbers is 2 x 29 = 58

Greatest Common Factor of 406,870 By Matching Biggest Common Factor Method

Now, list down the factors of 406

1,2,7,14,29,58,203,406

Now, list down the factors of 870

1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870

Greatest Common Factor

We found the factors 406,870 . The biggest common factor number is the GCF number.
So the greatest common factor 406,870 is 58.

Lets's calculate LCM of 396,513

Lowest Common Multiple of 396,513 using Common Division

3	396, 513
3	132, 171
	44, 57

∴ So the LCM of the given numbers is 3 x 3 x 44 x 57 = 22572

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 58/22572

Therefore, the GCF of Fractions 406/396,870/513 is 58/22572

Least Common Multiple of 396,513 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 396,513 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(396,513) = 9

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

GCF(396,513) x common factors =9 x 1 = 9

LCM(396,513) = ( 396 × 513 ) / 9

LCM(396,513) = 203148 / 9

LCM(396,513) = 22572

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FAQs on GCF of Fractions of 406/396, 870/513

1. What is the HCF of 406,870?

The HCF of 406,870 is 58

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 406/396, 870/513?

Answer: GCF of Numerators as per given numbers 406/396, 870/513 is

GCF of Numerators i.e. for 406,870 is 58

LCM of denominators i.e. for 396,513 is 22572.

Thus, GCF of Fractions is 58/22572.Finally, GCF of Fractions for 406/396, 870/513 is 58/22572.