How to Find GCF of 8419/216, 3886/1224?

GCF of 8419/216, 3886/1224

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 8419/216, 3886/1224 i.e 1/3672 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8419/216, 3886/1224.

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 8419/216,3886/1224?

Given fractions are 8419/216,3886/1224

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 8419/216,3886/1224, numerators are 8419,3886

Denominators are 216,1224

The GCF of 8419,3886 is 1 .

LCM of 216,1224 is 3672.

The greatest common factor of 8419/216,3886/1224 = [GCF of 8419,3886]/[LCM of 216,1224]= 1/3672

Therefore, the GCF of 8419/216,3886/1224 is 1/3672.

Greatest Common Factor of 8419,3886

To find the highest common factor of 8419,3886, we have to find the factors of both numbers and list the highest common factor.

The factors of 8419 are 1, 8419

The factors of 3886 are 1, 2, 29, 58, 67, 134, 1943, 3886

The HCF of 8419,3886 is 1.

Lets's calculate GCF of 8419,3886

Greatest Common Factor (GCF) of 8419,3886 By Common Division

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

Greatest Common Factor of 8419,3886 By Matching Biggest Common Factor Method

Now, list down the factors of 8419

1,8419

Now, list down the factors of 3886

1,2,29,58,67,134,1943,3886

Greatest Common Factor

We found the factors 8419,3886 . The biggest common factor number is the GCF number.
So the greatest common factor 8419,3886 is 1.

Lets's calculate LCM of 216,1224

Lowest Common Multiple of 216,1224 using Common Division

2	216, 1224
2	108, 612
2	54, 306
3	27, 153
3	9, 51
	3, 17

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 3 x 3 x 17 = 3672

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3672

Therefore, the GCF of Fractions 8419/216,3886/1224 is 1/3672

Least Common Multiple of 216,1224 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 216,1224 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(216,1224) = 72

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

GCF(216,1224) x common factors =72 x 1 = 72

LCM(216,1224) = ( 216 × 1224 ) / 72

LCM(216,1224) = 264384 / 72

LCM(216,1224) = 3672

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FAQs on GCF of Fractions of 8419/216, 3886/1224

1. What is the HCF of 8419,3886?

The HCF of 8419,3886 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 8419/216, 3886/1224?

Answer: GCF of Numerators as per given numbers 8419/216, 3886/1224 is

GCF of Numerators i.e. for 8419,3886 is 1

LCM of denominators i.e. for 216,1224 is 3672.

Thus, GCF of Fractions is 1/3672.Finally, GCF of Fractions for 8419/216, 3886/1224 is 1/3672.