How to Find GCF of 284/676, 5416/6871?

GCF of 284/676, 5416/6871

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 284/676, 5416/6871 i.e 4/4644796 easily. The following is the detailed procedure to determine the greatest common factor of fractions 284/676, 5416/6871.

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 284/676,5416/6871?

Given fractions are 284/676,5416/6871

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 284/676,5416/6871, numerators are 284,5416

Denominators are 676,6871

The GCF of 284,5416 is 4 .

LCM of 676,6871 is 4644796.

The greatest common factor of 284/676,5416/6871 = [GCF of 284,5416]/[LCM of 676,6871]= 4/4644796

Therefore, the GCF of 284/676,5416/6871 is 4/4644796.

Greatest Common Factor of 284,5416

To find the highest common factor of 284,5416, we have to find the factors of both numbers and list the highest common factor.

The factors of 284 are 1, 2, 4, 71, 142, 284

The factors of 5416 are 1, 2, 4, 8, 677, 1354, 2708, 5416

The HCF of 284,5416 is 4.

Lets's calculate GCF of 284,5416

Greatest Common Factor (GCF) of 284,5416 By Common Division

2	284, 5416
2	142, 2708
	71, 1354

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 284,5416 By Matching Biggest Common Factor Method

Now, list down the factors of 284

1,2,4,71,142,284

Now, list down the factors of 5416

1,2,4,8,677,1354,2708,5416

Greatest Common Factor

We found the factors 284,5416 . The biggest common factor number is the GCF number.
So the greatest common factor 284,5416 is 4.

Lets's calculate LCM of 676,6871

Lowest Common Multiple of 676,6871 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 4644796

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/4644796

Therefore, the GCF of Fractions 284/676,5416/6871 is 4/4644796

Least Common Multiple of 676,6871 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 676,6871 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(676,6871) = 1

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

GCF(676,6871) x common factors =1 x 1 = 1

LCM(676,6871) = ( 676 × 6871 ) / 1

LCM(676,6871) = 4644796 / 1

LCM(676,6871) = 4644796

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FAQs on GCF of Fractions of 284/676, 5416/6871

1. What is the HCF of 284,5416?

The HCF of 284,5416 is 4

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 284/676, 5416/6871?

Answer: GCF of Numerators as per given numbers 284/676, 5416/6871 is

GCF of Numerators i.e. for 284,5416 is 4

LCM of denominators i.e. for 676,6871 is 4644796.

Thus, GCF of Fractions is 4/4644796.Finally, GCF of Fractions for 284/676, 5416/6871 is 4/4644796.