How to Find GCF of 840/289, 3314/467?

GCF of 840/289, 3314/467

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 840/289, 3314/467 i.e 2/134963 easily. The following is the detailed procedure to determine the greatest common factor of fractions 840/289, 3314/467.

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 840/289,3314/467?

Given fractions are 840/289,3314/467

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 840/289,3314/467, numerators are 840,3314

Denominators are 289,467

The GCF of 840,3314 is 2 .

LCM of 289,467 is 134963.

The greatest common factor of 840/289,3314/467 = [GCF of 840,3314]/[LCM of 289,467]= 2/134963

Therefore, the GCF of 840/289,3314/467 is 2/134963.

Greatest Common Factor of 840,3314

To find the highest common factor of 840,3314, we have to find the factors of both numbers and list the highest common factor.

The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840

The factors of 3314 are 1, 2, 1657, 3314

The HCF of 840,3314 is 2.

Lets's calculate GCF of 840,3314

Greatest Common Factor (GCF) of 840,3314 By Common Division

2	840, 3314
	420, 1657

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

Greatest Common Factor of 840,3314 By Matching Biggest Common Factor Method

Now, list down the factors of 840

1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840

Now, list down the factors of 3314

1,2,1657,3314

Greatest Common Factor

We found the factors 840,3314 . The biggest common factor number is the GCF number.
So the greatest common factor 840,3314 is 2.

Lets's calculate LCM of 289,467

Lowest Common Multiple of 289,467 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 134963

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/134963

Therefore, the GCF of Fractions 840/289,3314/467 is 2/134963

Least Common Multiple of 289,467 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 289,467 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(289,467) = 1

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

GCF(289,467) x common factors =1 x 1 = 1

LCM(289,467) = ( 289 × 467 ) / 1

LCM(289,467) = 134963 / 1

LCM(289,467) = 134963

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FAQs on GCF of Fractions of 840/289, 3314/467

1. What is the HCF of 840,3314?

The HCF of 840,3314 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 840/289, 3314/467?

Answer: GCF of Numerators as per given numbers 840/289, 3314/467 is

GCF of Numerators i.e. for 840,3314 is 2

LCM of denominators i.e. for 289,467 is 134963.

Thus, GCF of Fractions is 2/134963.Finally, GCF of Fractions for 840/289, 3314/467 is 2/134963.