How to Find GCF of 412/91, 406/6922?

GCF of 412/91, 406/6922

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 412/91, 406/6922 i.e 2/629902 easily. The following is the detailed procedure to determine the greatest common factor of fractions 412/91, 406/6922.

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 412/91,406/6922?

Given fractions are 412/91,406/6922

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 412/91,406/6922, numerators are 412,406

Denominators are 91,6922

The GCF of 412,406 is 2 .

LCM of 91,6922 is 629902.

The greatest common factor of 412/91,406/6922 = [GCF of 412,406]/[LCM of 91,6922]= 2/629902

Therefore, the GCF of 412/91,406/6922 is 2/629902.

Greatest Common Factor of 412,406

To find the highest common factor of 412,406, we have to find the factors of both numbers and list the highest common factor.

The factors of 412 are 1, 2, 4, 103, 206, 412

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

The HCF of 412,406 is 2.

Lets's calculate GCF of 412,406

Greatest Common Factor (GCF) of 412,406 By Common Division

2	412, 406
	206, 203

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

Greatest Common Factor of 412,406 By Matching Biggest Common Factor Method

Now, list down the factors of 412

1,2,4,103,206,412

Now, list down the factors of 406

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

Greatest Common Factor

We found the factors 412,406 . The biggest common factor number is the GCF number.
So the greatest common factor 412,406 is 2.

Lets's calculate LCM of 91,6922

Lowest Common Multiple of 91,6922 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 629902

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/629902

Therefore, the GCF of Fractions 412/91,406/6922 is 2/629902

Least Common Multiple of 91,6922 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 91,6922 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(91,6922) = 1

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

GCF(91,6922) x common factors =1 x 1 = 1

LCM(91,6922) = ( 91 × 6922 ) / 1

LCM(91,6922) = 629902 / 1

LCM(91,6922) = 629902

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FAQs on GCF of Fractions of 412/91, 406/6922

1. What is the HCF of 412,406?

The HCF of 412,406 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 412/91, 406/6922?

Answer: GCF of Numerators as per given numbers 412/91, 406/6922 is

GCF of Numerators i.e. for 412,406 is 2

LCM of denominators i.e. for 91,6922 is 629902.

Thus, GCF of Fractions is 2/629902.Finally, GCF of Fractions for 412/91, 406/6922 is 2/629902.