GCF of 261/237, 870/756
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 261/237, 870/756 i.e 87/59724 easily. The following is the detailed procedure to determine the greatest common factor of fractions 261/237, 870/756.
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 261/237,870/756?
Given fractions are 261/237,870/756
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 261/237,870/756, numerators are 261,870
Denominators are 237,756
The GCF of 261,870 is 87 .
LCM of 237,756 is 59724.
The greatest common factor of 261/237,870/756 = [GCF of 261,870]/[LCM of 237,756]= 87/59724
Therefore, the GCF of 261/237,870/756 is 87/59724.
To find the highest common factor of 261,870, we have to find the factors of both numbers and list the highest common factor.
The factors of 261 are 1, 3, 9, 29, 87, 261
The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870
The HCF of 261,870 is 87.
Lets's calculate GCF of 261,870
| 3 | 261, 870 |
| 29 | 87, 290 |
| 3, 10 |
∴ So the GCF of the given numbers is 3 x 29 = 87
Greatest Common Factor of 261,870 By Matching Biggest Common Factor Method
Now, list down the factors of 261
:1,3,9,29,87,261
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 261,870 . The biggest common factor number is the GCF number.
So the greatest common factor 261,870 is 87.
Lets's calculate LCM of 237,756
| 3 | 237, 756 |
| 79, 252 |
∴ So the LCM of the given numbers is 3 x 79 x 252 = 59724
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 87/59724
Therefore, the GCF of Fractions 261/237,870/756 is 87/59724
Least Common Multiple of 237,756 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 237,756 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(237,756) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(237,756) x common factors =3 x 1 = 3
LCM(237,756) = ( 237 × 756 ) / 3
LCM(237,756) = 179172 / 3
LCM(237,756) = 59724
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FAQs on GCF of Fractions of 261/237, 870/756
1. What is the HCF of 261,870?
The HCF of 261,870 is 87
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 261/237, 870/756?
Answer: GCF of Numerators as per given numbers 261/237, 870/756 is
GCF of Numerators i.e. for 261,870 is 87
LCM of denominators i.e. for 237,756 is 59724.
Thus, GCF of Fractions is 87/59724.Finally, GCF of Fractions for 261/237, 870/756 is 87/59724.