How to Find GCF of 17/214, 75/460, 601/789?

GCF of 17/214, 75/460, 601/789

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 17/214, 75/460, 601/789 i.e 1/38834580 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/214, 75/460, 601/789.

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 17/214,75/460,601/789?

Given fractions are 17/214,75/460,601/789

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 17/214,75/460,601/789, numerators are 17,75,601

Denominators are 214,460,789

The GCF of 17,75,601 is 1 .

LCM of 214,460,789 is 38834580.

The greatest common factor of 17/214,75/460,601/789 = [GCF of 17,75,601]/[LCM of 214,460,789]= 1/38834580

Therefore, the GCF of 17/214,75/460,601/789 is 1/38834580.

Greatest Common Factor of 17,75,601

To find the highest common factor of 17,75,601, we have to find the factors of both numbers and list the highest common factor.

The factors of 17 are 1, 17

The factors of 75 are 1, 3, 5, 15, 25, 75

The factors of 601 are 1, 601

The HCF of 17,75,601 is 1.

Lets's calculate GCF of 17,75,601

Greatest Common Factor (GCF) of 17,75,601 By Common Division

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

Greatest Common Factor of 17,75,601 By Matching Biggest Common Factor Method

Now, list down the factors of 17

1,17

Now, list down the factors of 75

1,3,5,15,25,75

Now, list down the factors of 601

1,601

Greatest Common Factor

We found the factors 17,75,601 . The biggest common factor number is the GCF number.
So the greatest common factor 17,75,601 is 1.

Lets's calculate LCM of 214,460,789

Lowest Common Multiple of 214,460,789 using Common Division

2	214, 460, 789
	107, 230, 789

∴ So the LCM of the given numbers is 2 x 107 x 230 x 789 = 38834580

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/38834580

Therefore, the GCF of Fractions 17/214,75/460,601/789 is 1/38834580

Least Common Multiple of 214,460,789 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 214,460,789 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(214,460,789) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(214,460,789) x common factors =1 x 2 = 2

LCM(214,460,789) = ( 214 × 460 × 789 ) / 2

LCM(214,460,789) = 77669160 / 2

LCM(214,460,789) = 38834580

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FAQs on GCF of Fractions of 17/214, 75/460, 601/789

1. What is the HCF of 17,75,601?

The HCF of 17,75,601 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 17/214, 75/460, 601/789?

Answer: GCF of Numerators as per given numbers 17/214, 75/460, 601/789 is

GCF of Numerators i.e. for 17,75,601 is 1

LCM of denominators i.e. for 214,460,789 is 38834580.

Thus, GCF of Fractions is 1/38834580.Finally, GCF of Fractions for 17/214, 75/460, 601/789 is 1/38834580.