GCF of 810/70, 960/320
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 810/70, 960/320 i.e 30/2240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 810/70, 960/320.
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 810/70,960/320?
Given fractions are 810/70,960/320
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 810/70,960/320, numerators are 810,960
Denominators are 70,320
The GCF of 810,960 is 30 .
LCM of 70,320 is 2240.
The greatest common factor of 810/70,960/320 = [GCF of 810,960]/[LCM of 70,320]= 30/2240
Therefore, the GCF of 810/70,960/320 is 30/2240.
To find the highest common factor of 810,960, we have to find the factors of both numbers and list the highest common factor.
The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810
The factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
The HCF of 810,960 is 30.
Lets's calculate GCF of 810,960
| 2 | 810, 960 |
| 3 | 405, 480 |
| 5 | 135, 160 |
| 27, 32 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 810,960 By Matching Biggest Common Factor Method
Now, list down the factors of 810
:1,2,3,5,6,9,10,15,18,27,30,45,54,81,90,135,162,270,405,810
Now, list down the factors of 960
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,64,80,96,120,160,192,240,320,480,960
Greatest Common Factor
We found the factors 810,960 . The biggest common factor number is the GCF number.
So the greatest common factor 810,960 is 30.
Lets's calculate LCM of 70,320
| 2 | 70, 320 |
| 5 | 35, 160 |
| 7, 32 |
∴ So the LCM of the given numbers is 2 x 5 x 7 x 32 = 2240
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/2240
Therefore, the GCF of Fractions 810/70,960/320 is 30/2240
Least Common Multiple of 70,320 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 70,320 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,320) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(70,320) x common factors =10 x 1 = 10
LCM(70,320) = ( 70 × 320 ) / 10
LCM(70,320) = 22400 / 10
LCM(70,320) = 2240
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 810/70, 960/320
1. What is the HCF of 810,960?
The HCF of 810,960 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 810/70, 960/320?
Answer: GCF of Numerators as per given numbers 810/70, 960/320 is
GCF of Numerators i.e. for 810,960 is 30
LCM of denominators i.e. for 70,320 is 2240.
Thus, GCF of Fractions is 30/2240.Finally, GCF of Fractions for 810/70, 960/320 is 30/2240.