How to Find GCF of 82/65, 51/90, 211/702?

GCF of 82/65, 51/90, 211/702

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 82/65, 51/90, 211/702 i.e 1/3510 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/65, 51/90, 211/702.

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 82/65,51/90,211/702?

Given fractions are 82/65,51/90,211/702

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 82/65,51/90,211/702, numerators are 82,51,211

Denominators are 65,90,702

The GCF of 82,51,211 is 1 .

LCM of 65,90,702 is 3510.

The greatest common factor of 82/65,51/90,211/702 = [GCF of 82,51,211]/[LCM of 65,90,702]= 1/3510

Therefore, the GCF of 82/65,51/90,211/702 is 1/3510.

Greatest Common Factor of 82,51,211

To find the highest common factor of 82,51,211, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 51 are 1, 3, 17, 51

The factors of 211 are 1, 211

The HCF of 82,51,211 is 1.

Lets's calculate GCF of 82,51,211

Greatest Common Factor (GCF) of 82,51,211 By Common Division

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

Greatest Common Factor of 82,51,211 By Matching Biggest Common Factor Method

Now, list down the factors of 82

1,2,41,82

Now, list down the factors of 51

1,3,17,51

Now, list down the factors of 211

1,211

Greatest Common Factor

We found the factors 82,51,211 . The biggest common factor number is the GCF number.
So the greatest common factor 82,51,211 is 1.

Lets's calculate LCM of 65,90,702

Lowest Common Multiple of 65,90,702 using Common Division

2	65, 90, 702
3	65, 45, 351
3	65, 15, 117
5	65, 5, 39
13	13, 1, 39
	1, 1, 3

∴ So the LCM of the given numbers is 2 x 3 x 3 x 5 x 13 x 1 x 1 x 3 = 3510

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3510

Therefore, the GCF of Fractions 82/65,51/90,211/702 is 1/3510

Least Common Multiple of 65,90,702 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 65,90,702 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,90,702) = 1

common factors(in case of two or more numbers have common factors) = 1170

GCF(65,90,702) x common factors =1 x 1170 = 1170

LCM(65,90,702) = ( 65 × 90 × 702 ) / 1170

LCM(65,90,702) = 4106700 / 1170

LCM(65,90,702) = 3510

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 82/65, 51/90, 211/702

1. What is the HCF of 82,51,211?

The HCF of 82,51,211 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 82/65, 51/90, 211/702?

Answer: GCF of Numerators as per given numbers 82/65, 51/90, 211/702 is

GCF of Numerators i.e. for 82,51,211 is 1

LCM of denominators i.e. for 65,90,702 is 3510.

Thus, GCF of Fractions is 1/3510.Finally, GCF of Fractions for 82/65, 51/90, 211/702 is 1/3510.