How to Find GCF of 812/12, 421/1219?

GCF of 812/12, 421/1219

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 812/12, 421/1219 i.e 1/14628 easily. The following is the detailed procedure to determine the greatest common factor of fractions 812/12, 421/1219.

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 812/12,421/1219?

Given fractions are 812/12,421/1219

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 812/12,421/1219, numerators are 812,421

Denominators are 12,1219

The GCF of 812,421 is 1 .

LCM of 12,1219 is 14628.

The greatest common factor of 812/12,421/1219 = [GCF of 812,421]/[LCM of 12,1219]= 1/14628

Therefore, the GCF of 812/12,421/1219 is 1/14628.

Greatest Common Factor of 812,421

To find the highest common factor of 812,421, we have to find the factors of both numbers and list the highest common factor.

The factors of 812 are 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812

The factors of 421 are 1, 421

The HCF of 812,421 is 1.

Lets's calculate GCF of 812,421

Greatest Common Factor (GCF) of 812,421 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 812,421 By Matching Biggest Common Factor Method

Now, list down the factors of 812

1,2,4,7,14,28,29,58,116,203,406,812

Now, list down the factors of 421

1,421

Greatest Common Factor

We found the factors 812,421 . The biggest common factor number is the GCF number.
So the greatest common factor 812,421 is 1.

Lets's calculate LCM of 12,1219

Lowest Common Multiple of 12,1219 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 14628

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/14628

Therefore, the GCF of Fractions 812/12,421/1219 is 1/14628

Least Common Multiple of 12,1219 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 12,1219 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(12,1219) = 1

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

GCF(12,1219) x common factors =1 x 1 = 1

LCM(12,1219) = ( 12 × 1219 ) / 1

LCM(12,1219) = 14628 / 1

LCM(12,1219) = 14628

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FAQs on GCF of Fractions of 812/12, 421/1219

1. What is the HCF of 812,421?

The HCF of 812,421 is 1

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 812/12, 421/1219?

Answer: GCF of Numerators as per given numbers 812/12, 421/1219 is

GCF of Numerators i.e. for 812,421 is 1

LCM of denominators i.e. for 12,1219 is 14628.

Thus, GCF of Fractions is 1/14628.Finally, GCF of Fractions for 812/12, 421/1219 is 1/14628.