How to Find GCF of 86/65, 17/180, 278/994?

GCF of 86/65, 17/180, 278/994

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 86/65, 17/180, 278/994 i.e 1/1162980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 86/65, 17/180, 278/994.

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 86/65,17/180,278/994?

Given fractions are 86/65,17/180,278/994

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 86/65,17/180,278/994, numerators are 86,17,278

Denominators are 65,180,994

The GCF of 86,17,278 is 1 .

LCM of 65,180,994 is 1162980.

The greatest common factor of 86/65,17/180,278/994 = [GCF of 86,17,278]/[LCM of 65,180,994]= 1/1162980

Therefore, the GCF of 86/65,17/180,278/994 is 1/1162980.

Greatest Common Factor of 86,17,278

To find the highest common factor of 86,17,278, we have to find the factors of both numbers and list the highest common factor.

The factors of 86 are 1, 2, 43, 86

The factors of 17 are 1, 17

The factors of 278 are 1, 2, 139, 278

The HCF of 86,17,278 is 1.

Lets's calculate GCF of 86,17,278

Greatest Common Factor (GCF) of 86,17,278 By Common Division

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

Greatest Common Factor of 86,17,278 By Matching Biggest Common Factor Method

Now, list down the factors of 86

1,2,43,86

Now, list down the factors of 17

1,17

Now, list down the factors of 278

1,2,139,278

Greatest Common Factor

We found the factors 86,17,278 . The biggest common factor number is the GCF number.
So the greatest common factor 86,17,278 is 1.

Lets's calculate LCM of 65,180,994

Lowest Common Multiple of 65,180,994 using Common Division

2	65, 180, 994
5	65, 90, 497
	13, 18, 497

∴ So the LCM of the given numbers is 2 x 5 x 13 x 18 x 497 = 1162980

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1162980

Therefore, the GCF of Fractions 86/65,17/180,278/994 is 1/1162980

Least Common Multiple of 65,180,994 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 65,180,994 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,180,994) = 1

common factors(in case of two or more numbers have common factors) = 10

GCF(65,180,994) x common factors =1 x 10 = 10

LCM(65,180,994) = ( 65 × 180 × 994 ) / 10

LCM(65,180,994) = 11629800 / 10

LCM(65,180,994) = 1162980

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FAQs on GCF of Fractions of 86/65, 17/180, 278/994

1. What is the HCF of 86,17,278?

The HCF of 86,17,278 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 86/65, 17/180, 278/994?

Answer: GCF of Numerators as per given numbers 86/65, 17/180, 278/994 is

GCF of Numerators i.e. for 86,17,278 is 1

LCM of denominators i.e. for 65,180,994 is 1162980.

Thus, GCF of Fractions is 1/1162980.Finally, GCF of Fractions for 86/65, 17/180, 278/994 is 1/1162980.