How to Find GCF of 900/199, 870/763?

GCF of 900/199, 870/763

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 900/199, 870/763 i.e 30/151837 easily. The following is the detailed procedure to determine the greatest common factor of fractions 900/199, 870/763.

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 900/199,870/763?

Given fractions are 900/199,870/763

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 900/199,870/763, numerators are 900,870

Denominators are 199,763

The GCF of 900,870 is 30 .

LCM of 199,763 is 151837.

The greatest common factor of 900/199,870/763 = [GCF of 900,870]/[LCM of 199,763]= 30/151837

Therefore, the GCF of 900/199,870/763 is 30/151837.

Greatest Common Factor of 900,870

To find the highest common factor of 900,870, we have to find the factors of both numbers and list the highest common factor.

The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900

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

The HCF of 900,870 is 30.

Lets's calculate GCF of 900,870

Greatest Common Factor (GCF) of 900,870 By Common Division

2	900, 870
3	450, 435
5	150, 145
	30, 29

∴ So the GCF of the given numbers is 2 x 3 x 5 = 30

Greatest Common Factor of 900,870 By Matching Biggest Common Factor Method

Now, list down the factors of 900

1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450,900

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 900,870 . The biggest common factor number is the GCF number.
So the greatest common factor 900,870 is 30.

Lets's calculate LCM of 199,763

Lowest Common Multiple of 199,763 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 151837

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/151837

Therefore, the GCF of Fractions 900/199,870/763 is 30/151837

Least Common Multiple of 199,763 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 199,763 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(199,763) = 1

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

GCF(199,763) x common factors =1 x 1 = 1

LCM(199,763) = ( 199 × 763 ) / 1

LCM(199,763) = 151837 / 1

LCM(199,763) = 151837

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FAQs on GCF of Fractions of 900/199, 870/763

1. What is the HCF of 900,870?

The HCF of 900,870 is 30

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 900/199, 870/763?

Answer: GCF of Numerators as per given numbers 900/199, 870/763 is

GCF of Numerators i.e. for 900,870 is 30

LCM of denominators i.e. for 199,763 is 151837.

Thus, GCF of Fractions is 30/151837.Finally, GCF of Fractions for 900/199, 870/763 is 30/151837.