GCF of 2160/705, 8454/7944
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2160/705, 8454/7944 i.e 6/1866840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2160/705, 8454/7944.
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 2160/705,8454/7944?
Given fractions are 2160/705,8454/7944
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 2160/705,8454/7944, numerators are 2160,8454
Denominators are 705,7944
The GCF of 2160,8454 is 6 .
LCM of 705,7944 is 1866840.
The greatest common factor of 2160/705,8454/7944 = [GCF of 2160,8454]/[LCM of 705,7944]= 6/1866840
Therefore, the GCF of 2160/705,8454/7944 is 6/1866840.
To find the highest common factor of 2160,8454, 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 8454 are 1, 2, 3, 6, 1409, 2818, 4227, 8454
The HCF of 2160,8454 is 6.
Lets's calculate GCF of 2160,8454
| 2 | 2160, 8454 |
| 3 | 1080, 4227 |
| 360, 1409 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 2160,8454 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 8454
:1,2,3,6,1409,2818,4227,8454
Greatest Common Factor
We found the factors 2160,8454 . The biggest common factor number is the GCF number.
So the greatest common factor 2160,8454 is 6.
Lets's calculate LCM of 705,7944
| 3 | 705, 7944 |
| 235, 2648 |
∴ So the LCM of the given numbers is 3 x 235 x 2648 = 1866840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/1866840
Therefore, the GCF of Fractions 2160/705,8454/7944 is 6/1866840
Least Common Multiple of 705,7944 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 705,7944 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(705,7944) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(705,7944) x common factors =3 x 1 = 3
LCM(705,7944) = ( 705 × 7944 ) / 3
LCM(705,7944) = 5600520 / 3
LCM(705,7944) = 1866840
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FAQs on GCF of Fractions of 2160/705, 8454/7944
1. What is the HCF of 2160,8454?
The HCF of 2160,8454 is 6
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 2160/705, 8454/7944?
Answer: GCF of Numerators as per given numbers 2160/705, 8454/7944 is
GCF of Numerators i.e. for 2160,8454 is 6
LCM of denominators i.e. for 705,7944 is 1866840.
Thus, GCF of Fractions is 6/1866840.Finally, GCF of Fractions for 2160/705, 8454/7944 is 6/1866840.