GCF of 2160/517, 3972/374
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2160/517, 3972/374 i.e 12/17578 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2160/517, 3972/374.
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 2160/517,3972/374?
Given fractions are 2160/517,3972/374
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 2160/517,3972/374, numerators are 2160,3972
Denominators are 517,374
The GCF of 2160,3972 is 12 .
LCM of 517,374 is 17578.
The greatest common factor of 2160/517,3972/374 = [GCF of 2160,3972]/[LCM of 517,374]= 12/17578
Therefore, the GCF of 2160/517,3972/374 is 12/17578.
To find the highest common factor of 2160,3972, we have to find the factors of both numbers and list the highest common factor.
The factors of 2160 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 36, 40, 45, 48, 54, 60, 72, 80, 90, 108, 120, 135, 144, 180, 216, 240, 270, 360, 432, 540, 720, 1080, 2160
The factors of 3972 are 1, 2, 3, 4, 6, 12, 331, 662, 993, 1324, 1986, 3972
The HCF of 2160,3972 is 12.
Lets's calculate GCF of 2160,3972
| 2 | 2160, 3972 |
| 2 | 1080, 1986 |
| 3 | 540, 993 |
| 180, 331 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 2160,3972 By Matching Biggest Common Factor Method
Now, list down the factors of 2160
:1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,27,30,36,40,45,48,54,60,72,80,90,108,120,135,144,180,216,240,270,360,432,540,720,1080,2160
Now, list down the factors of 3972
:1,2,3,4,6,12,331,662,993,1324,1986,3972
Greatest Common Factor
We found the factors 2160,3972 . The biggest common factor number is the GCF number.
So the greatest common factor 2160,3972 is 12.
Lets's calculate LCM of 517,374
| 11 | 517, 374 |
| 47, 34 |
∴ So the LCM of the given numbers is 11 x 47 x 34 = 17578
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/17578
Therefore, the GCF of Fractions 2160/517,3972/374 is 12/17578
Least Common Multiple of 517,374 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 517,374 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(517,374) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(517,374) x common factors =11 x 1 = 11
LCM(517,374) = ( 517 × 374 ) / 11
LCM(517,374) = 193358 / 11
LCM(517,374) = 17578
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 2160/517, 3972/374
1. What is the HCF of 2160,3972?
The HCF of 2160,3972 is 12
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 2160/517, 3972/374?
Answer: GCF of Numerators as per given numbers 2160/517, 3972/374 is
GCF of Numerators i.e. for 2160,3972 is 12
LCM of denominators i.e. for 517,374 is 17578.
Thus, GCF of Fractions is 12/17578.Finally, GCF of Fractions for 2160/517, 3972/374 is 12/17578.