GCF of 2565/756, 2238/1720
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2565/756, 2238/1720 i.e 3/325080 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2565/756, 2238/1720.
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 2565/756,2238/1720?
Given fractions are 2565/756,2238/1720
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 2565/756,2238/1720, numerators are 2565,2238
Denominators are 756,1720
The GCF of 2565,2238 is 3 .
LCM of 756,1720 is 325080.
The greatest common factor of 2565/756,2238/1720 = [GCF of 2565,2238]/[LCM of 756,1720]= 3/325080
Therefore, the GCF of 2565/756,2238/1720 is 3/325080.
To find the highest common factor of 2565,2238, we have to find the factors of both numbers and list the highest common factor.
The factors of 2565 are 1, 3, 5, 9, 15, 19, 27, 45, 57, 95, 135, 171, 285, 513, 855, 2565
The factors of 2238 are 1, 2, 3, 6, 373, 746, 1119, 2238
The HCF of 2565,2238 is 3.
Lets's calculate GCF of 2565,2238
| 3 | 2565, 2238 |
| 855, 746 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 2565,2238 By Matching Biggest Common Factor Method
Now, list down the factors of 2565
:1,3,5,9,15,19,27,45,57,95,135,171,285,513,855,2565
Now, list down the factors of 2238
:1,2,3,6,373,746,1119,2238
Greatest Common Factor
We found the factors 2565,2238 . The biggest common factor number is the GCF number.
So the greatest common factor 2565,2238 is 3.
Lets's calculate LCM of 756,1720
| 2 | 756, 1720 |
| 2 | 378, 860 |
| 189, 430 |
∴ So the LCM of the given numbers is 2 x 2 x 189 x 430 = 325080
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/325080
Therefore, the GCF of Fractions 2565/756,2238/1720 is 3/325080
Least Common Multiple of 756,1720 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 756,1720 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(756,1720) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(756,1720) x common factors =4 x 1 = 4
LCM(756,1720) = ( 756 × 1720 ) / 4
LCM(756,1720) = 1300320 / 4
LCM(756,1720) = 325080
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FAQs on GCF of Fractions of 2565/756, 2238/1720
1. What is the HCF of 2565,2238?
The HCF of 2565,2238 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 2565/756, 2238/1720?
Answer: GCF of Numerators as per given numbers 2565/756, 2238/1720 is
GCF of Numerators i.e. for 2565,2238 is 3
LCM of denominators i.e. for 756,1720 is 325080.
Thus, GCF of Fractions is 3/325080.Finally, GCF of Fractions for 2565/756, 2238/1720 is 3/325080.