How to Find GCF of 85/12, 404/21, 259/550?

GCF of 85/12, 404/21, 259/550

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 85/12, 404/21, 259/550 i.e 1/23100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 85/12, 404/21, 259/550.

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 85/12,404/21,259/550?

Given fractions are 85/12,404/21,259/550

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 85/12,404/21,259/550, numerators are 85,404,259

Denominators are 12,21,550

The GCF of 85,404,259 is 1 .

LCM of 12,21,550 is 23100.

The greatest common factor of 85/12,404/21,259/550 = [GCF of 85,404,259]/[LCM of 12,21,550]= 1/23100

Therefore, the GCF of 85/12,404/21,259/550 is 1/23100.

Greatest Common Factor of 85,404,259

To find the highest common factor of 85,404,259, we have to find the factors of both numbers and list the highest common factor.

The factors of 85 are 1, 5, 17, 85

The factors of 404 are 1, 2, 4, 101, 202, 404

The factors of 259 are 1, 7, 37, 259

The HCF of 85,404,259 is 1.

Lets's calculate GCF of 85,404,259

Greatest Common Factor (GCF) of 85,404,259 By Common Division

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

Greatest Common Factor of 85,404,259 By Matching Biggest Common Factor Method

Now, list down the factors of 85

1,5,17,85

Now, list down the factors of 404

1,2,4,101,202,404

Now, list down the factors of 259

1,7,37,259

Greatest Common Factor

We found the factors 85,404,259 . The biggest common factor number is the GCF number.
So the greatest common factor 85,404,259 is 1.

Lets's calculate LCM of 12,21,550

Lowest Common Multiple of 12,21,550 using Common Division

2	12, 21, 550
3	6, 21, 275
	2, 7, 275

∴ So the LCM of the given numbers is 2 x 3 x 2 x 7 x 275 = 23100

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/23100

Therefore, the GCF of Fractions 85/12,404/21,259/550 is 1/23100

Least Common Multiple of 12,21,550 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 12,21,550 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(12,21,550) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(12,21,550) x common factors =1 x 6 = 6

LCM(12,21,550) = ( 12 × 21 × 550 ) / 6

LCM(12,21,550) = 138600 / 6

LCM(12,21,550) = 23100

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FAQs on GCF of Fractions of 85/12, 404/21, 259/550

1. What is the HCF of 85,404,259?

The HCF of 85,404,259 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 85/12, 404/21, 259/550?

Answer: GCF of Numerators as per given numbers 85/12, 404/21, 259/550 is

GCF of Numerators i.e. for 85,404,259 is 1

LCM of denominators i.e. for 12,21,550 is 23100.

Thus, GCF of Fractions is 1/23100.Finally, GCF of Fractions for 85/12, 404/21, 259/550 is 1/23100.