How to Find GCF of 3362/289, 6816/384?

GCF of 3362/289, 6816/384

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 3362/289, 6816/384 i.e 2/110976 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3362/289, 6816/384.

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 3362/289,6816/384?

Given fractions are 3362/289,6816/384

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 3362/289,6816/384, numerators are 3362,6816

Denominators are 289,384

The GCF of 3362,6816 is 2 .

LCM of 289,384 is 110976.

The greatest common factor of 3362/289,6816/384 = [GCF of 3362,6816]/[LCM of 289,384]= 2/110976

Therefore, the GCF of 3362/289,6816/384 is 2/110976.

Greatest Common Factor of 3362,6816

To find the highest common factor of 3362,6816, we have to find the factors of both numbers and list the highest common factor.

The factors of 3362 are 1, 2, 41, 82, 1681, 3362

The factors of 6816 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 71, 96, 142, 213, 284, 426, 568, 852, 1136, 1704, 2272, 3408, 6816

The HCF of 3362,6816 is 2.

Lets's calculate GCF of 3362,6816

Greatest Common Factor (GCF) of 3362,6816 By Common Division

2	3362, 6816
	1681, 3408

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

Greatest Common Factor of 3362,6816 By Matching Biggest Common Factor Method

Now, list down the factors of 3362

1,2,41,82,1681,3362

Now, list down the factors of 6816

1,2,3,4,6,8,12,16,24,32,48,71,96,142,213,284,426,568,852,1136,1704,2272,3408,6816

Greatest Common Factor

We found the factors 3362,6816 . The biggest common factor number is the GCF number.
So the greatest common factor 3362,6816 is 2.

Lets's calculate LCM of 289,384

Lowest Common Multiple of 289,384 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 110976

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/110976

Therefore, the GCF of Fractions 3362/289,6816/384 is 2/110976

Least Common Multiple of 289,384 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 289,384 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(289,384) = 1

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

GCF(289,384) x common factors =1 x 1 = 1

LCM(289,384) = ( 289 × 384 ) / 1

LCM(289,384) = 110976 / 1

LCM(289,384) = 110976

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FAQs on GCF of Fractions of 3362/289, 6816/384

1. What is the HCF of 3362,6816?

The HCF of 3362,6816 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 3362/289, 6816/384?

Answer: GCF of Numerators as per given numbers 3362/289, 6816/384 is

GCF of Numerators i.e. for 3362,6816 is 2

LCM of denominators i.e. for 289,384 is 110976.

Thus, GCF of Fractions is 2/110976.Finally, GCF of Fractions for 3362/289, 6816/384 is 2/110976.