How to Find GCF of 819/604, 870/991?

GCF of 819/604, 870/991

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 819/604, 870/991 i.e 3/598564 easily. The following is the detailed procedure to determine the greatest common factor of fractions 819/604, 870/991.

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 819/604,870/991?

Given fractions are 819/604,870/991

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 819/604,870/991, numerators are 819,870

Denominators are 604,991

The GCF of 819,870 is 3 .

LCM of 604,991 is 598564.

The greatest common factor of 819/604,870/991 = [GCF of 819,870]/[LCM of 604,991]= 3/598564

Therefore, the GCF of 819/604,870/991 is 3/598564.

Greatest Common Factor of 819,870

To find the highest common factor of 819,870, we have to find the factors of both numbers and list the highest common factor.

The factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819

The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870

The HCF of 819,870 is 3.

Lets's calculate GCF of 819,870

Greatest Common Factor (GCF) of 819,870 By Common Division

3	819, 870
	273, 290

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 819,870 By Matching Biggest Common Factor Method

Now, list down the factors of 819

1,3,7,9,13,21,39,63,91,117,273,819

Now, list down the factors of 870

1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870

Greatest Common Factor

We found the factors 819,870 . The biggest common factor number is the GCF number.
So the greatest common factor 819,870 is 3.

Lets's calculate LCM of 604,991

Lowest Common Multiple of 604,991 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 598564

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/598564

Therefore, the GCF of Fractions 819/604,870/991 is 3/598564

Least Common Multiple of 604,991 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 604,991 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(604,991) = 1

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

GCF(604,991) x common factors =1 x 1 = 1

LCM(604,991) = ( 604 × 991 ) / 1

LCM(604,991) = 598564 / 1

LCM(604,991) = 598564

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FAQs on GCF of Fractions of 819/604, 870/991

1. What is the HCF of 819,870?

The HCF of 819,870 is 3

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 819/604, 870/991?

Answer: GCF of Numerators as per given numbers 819/604, 870/991 is

GCF of Numerators i.e. for 819,870 is 3

LCM of denominators i.e. for 604,991 is 598564.

Thus, GCF of Fractions is 3/598564.Finally, GCF of Fractions for 819/604, 870/991 is 3/598564.