GCF of 837/54, 975/720
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 837/54, 975/720 i.e 3/2160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 837/54, 975/720.
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 837/54,975/720?
Given fractions are 837/54,975/720
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 837/54,975/720, numerators are 837,975
Denominators are 54,720
The GCF of 837,975 is 3 .
LCM of 54,720 is 2160.
The greatest common factor of 837/54,975/720 = [GCF of 837,975]/[LCM of 54,720]= 3/2160
Therefore, the GCF of 837/54,975/720 is 3/2160.
To find the highest common factor of 837,975, we have to find the factors of both numbers and list the highest common factor.
The factors of 837 are 1, 3, 9, 27, 31, 93, 279, 837
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The HCF of 837,975 is 3.
Lets's calculate GCF of 837,975
| 3 | 837, 975 |
| 279, 325 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 837,975 By Matching Biggest Common Factor Method
Now, list down the factors of 837
:1,3,9,27,31,93,279,837
Now, list down the factors of 975
:1,3,5,13,15,25,39,65,75,195,325,975
Greatest Common Factor
We found the factors 837,975 . The biggest common factor number is the GCF number.
So the greatest common factor 837,975 is 3.
Lets's calculate LCM of 54,720
| 2 | 54, 720 |
| 3 | 27, 360 |
| 3 | 9, 120 |
| 3, 40 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 40 = 2160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/2160
Therefore, the GCF of Fractions 837/54,975/720 is 3/2160
Least Common Multiple of 54,720 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 54,720 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,720) = 18
common factors(in case of two or more numbers have common factors) = 1
GCF(54,720) x common factors =18 x 1 = 18
LCM(54,720) = ( 54 × 720 ) / 18
LCM(54,720) = 38880 / 18
LCM(54,720) = 2160
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FAQs on GCF of Fractions of 837/54, 975/720
1. What is the HCF of 837,975?
The HCF of 837,975 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 837/54, 975/720?
Answer: GCF of Numerators as per given numbers 837/54, 975/720 is
GCF of Numerators i.e. for 837,975 is 3
LCM of denominators i.e. for 54,720 is 2160.
Thus, GCF of Fractions is 3/2160.Finally, GCF of Fractions for 837/54, 975/720 is 3/2160.