GCF of 2580/728, 2968/140
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2580/728, 2968/140 i.e 4/3640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2580/728, 2968/140.
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 2580/728,2968/140?
Given fractions are 2580/728,2968/140
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 2580/728,2968/140, numerators are 2580,2968
Denominators are 728,140
The GCF of 2580,2968 is 4 .
LCM of 728,140 is 3640.
The greatest common factor of 2580/728,2968/140 = [GCF of 2580,2968]/[LCM of 728,140]= 4/3640
Therefore, the GCF of 2580/728,2968/140 is 4/3640.
To find the highest common factor of 2580,2968, we have to find the factors of both numbers and list the highest common factor.
The factors of 2580 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 43, 60, 86, 129, 172, 215, 258, 430, 516, 645, 860, 1290, 2580
The factors of 2968 are 1, 2, 4, 7, 8, 14, 28, 53, 56, 106, 212, 371, 424, 742, 1484, 2968
The HCF of 2580,2968 is 4.
Lets's calculate GCF of 2580,2968
| 2 | 2580, 2968 |
| 2 | 1290, 1484 |
| 645, 742 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 2580,2968 By Matching Biggest Common Factor Method
Now, list down the factors of 2580
:1,2,3,4,5,6,10,12,15,20,30,43,60,86,129,172,215,258,430,516,645,860,1290,2580
Now, list down the factors of 2968
:1,2,4,7,8,14,28,53,56,106,212,371,424,742,1484,2968
Greatest Common Factor
We found the factors 2580,2968 . The biggest common factor number is the GCF number.
So the greatest common factor 2580,2968 is 4.
Lets's calculate LCM of 728,140
| 2 | 728, 140 |
| 2 | 364, 70 |
| 7 | 182, 35 |
| 26, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 26 x 5 = 3640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/3640
Therefore, the GCF of Fractions 2580/728,2968/140 is 4/3640
Least Common Multiple of 728,140 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 728,140 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(728,140) = 28
common factors(in case of two or more numbers have common factors) = 1
GCF(728,140) x common factors =28 x 1 = 28
LCM(728,140) = ( 728 × 140 ) / 28
LCM(728,140) = 101920 / 28
LCM(728,140) = 3640
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FAQs on GCF of Fractions of 2580/728, 2968/140
1. What is the HCF of 2580,2968?
The HCF of 2580,2968 is 4
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 2580/728, 2968/140?
Answer: GCF of Numerators as per given numbers 2580/728, 2968/140 is
GCF of Numerators i.e. for 2580,2968 is 4
LCM of denominators i.e. for 728,140 is 3640.
Thus, GCF of Fractions is 4/3640.Finally, GCF of Fractions for 2580/728, 2968/140 is 4/3640.