How to Find GCF of 1984/854, 6827/442?

GCF of 1984/854, 6827/442

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 1984/854, 6827/442 i.e 1/188734 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1984/854, 6827/442.

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 1984/854,6827/442?

Given fractions are 1984/854,6827/442

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 1984/854,6827/442, numerators are 1984,6827

Denominators are 854,442

The GCF of 1984,6827 is 1 .

LCM of 854,442 is 188734.

The greatest common factor of 1984/854,6827/442 = [GCF of 1984,6827]/[LCM of 854,442]= 1/188734

Therefore, the GCF of 1984/854,6827/442 is 1/188734.

Greatest Common Factor of 1984,6827

To find the highest common factor of 1984,6827, we have to find the factors of both numbers and list the highest common factor.

The factors of 1984 are 1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, 992, 1984

The factors of 6827 are 1, 6827

The HCF of 1984,6827 is 1.

Lets's calculate GCF of 1984,6827

Greatest Common Factor (GCF) of 1984,6827 By Common Division

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

Greatest Common Factor of 1984,6827 By Matching Biggest Common Factor Method

Now, list down the factors of 1984

1,2,4,8,16,31,32,62,64,124,248,496,992,1984

Now, list down the factors of 6827

1,6827

Greatest Common Factor

We found the factors 1984,6827 . The biggest common factor number is the GCF number.
So the greatest common factor 1984,6827 is 1.

Lets's calculate LCM of 854,442

Lowest Common Multiple of 854,442 using Common Division

2	854, 442
	427, 221

∴ So the LCM of the given numbers is 2 x 427 x 221 = 188734

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/188734

Therefore, the GCF of Fractions 1984/854,6827/442 is 1/188734

Least Common Multiple of 854,442 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 854,442 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(854,442) = 2

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

GCF(854,442) x common factors =2 x 1 = 2

LCM(854,442) = ( 854 × 442 ) / 2

LCM(854,442) = 377468 / 2

LCM(854,442) = 188734

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FAQs on GCF of Fractions of 1984/854, 6827/442

1. What is the HCF of 1984,6827?

The HCF of 1984,6827 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 1984/854, 6827/442?

Answer: GCF of Numerators as per given numbers 1984/854, 6827/442 is

GCF of Numerators i.e. for 1984,6827 is 1

LCM of denominators i.e. for 854,442 is 188734.

Thus, GCF of Fractions is 1/188734.Finally, GCF of Fractions for 1984/854, 6827/442 is 1/188734.