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GCF of 210/82, 216/5274

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 210/82, 216/5274 i.e 6/216234 easily. The following is the detailed procedure to determine the greatest common factor of fractions 210/82, 216/5274.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 210/82,216/5274?

Given fractions are 210/82,216/5274

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 210/82,216/5274, numerators are 210,216

Denominators are 82,5274

The GCF of 210,216 is 6 .

LCM of 82,5274 is 216234.

The greatest common factor of 210/82,216/5274 = [GCF of 210,216]/[LCM of 82,5274]= 6/216234

Therefore, the GCF of 210/82,216/5274 is 6/216234.

Greatest Common Factor of 210,216

To find the highest common factor of 210,216, we have to find the factors of both numbers and list the highest common factor.

The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216

The HCF of 210,216 is 6.

Lets's calculate GCF of 210,216

Greatest Common Factor (GCF) of 210,216 By Common Division

2 210, 216
3 105, 108
35, 36

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 210,216 By Matching Biggest Common Factor Method

Greatest Common Factor of 210,216 By Matching Biggest Common Factor Method

Now, list down the factors of 210

:

1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210

Now, list down the factors of 216

:

1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216

Greatest Common Factor

We found the factors 210,216 . The biggest common factor number is the GCF number.
So the greatest common factor 210,216 is 6.


Lets's calculate LCM of 82,5274

Lowest Common Multiple of 82,5274 using Common Division

2 82, 5274
41, 2637

∴ So the LCM of the given numbers is 2 x 41 x 2637 = 216234

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/216234

Therefore, the GCF of Fractions 210/82,216/5274 is 6/216234

Least Common Multiple of 82,5274 with GCF Formula

Least Common Multiple of 82,5274 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 82,5274 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(82,5274) = 2

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

GCF(82,5274) x common factors =2 x 1 = 2

LCM(82,5274) = ( 82 × 5274 ) / 2

LCM(82,5274) = 432468 / 2

LCM(82,5274) = 216234


GCF of Fractions Calculation Examples

FAQs on GCF of Fractions of 210/82, 216/5274

1. What is the HCF of 210,216?

The HCF of 210,216 is 6

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 210/82, 216/5274?

Answer: GCF of Numerators as per given numbers 210/82, 216/5274 is

GCF of Numerators i.e. for 210,216 is 6

LCM of denominators i.e. for 82,5274 is 216234.

Thus, GCF of Fractions is 6/216234.Finally, GCF of Fractions for 210/82, 216/5274 is 6/216234.