GCF of 1300/872, 2296/2656
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1300/872, 2296/2656 i.e 4/289504 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1300/872, 2296/2656.
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 1300/872,2296/2656?
Given fractions are 1300/872,2296/2656
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 1300/872,2296/2656, numerators are 1300,2296
Denominators are 872,2656
The GCF of 1300,2296 is 4 .
LCM of 872,2656 is 289504.
The greatest common factor of 1300/872,2296/2656 = [GCF of 1300,2296]/[LCM of 872,2656]= 4/289504
Therefore, the GCF of 1300/872,2296/2656 is 4/289504.
To find the highest common factor of 1300,2296, we have to find the factors of both numbers and list the highest common factor.
The factors of 1300 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, 1300
The factors of 2296 are 1, 2, 4, 7, 8, 14, 28, 41, 56, 82, 164, 287, 328, 574, 1148, 2296
The HCF of 1300,2296 is 4.
Lets's calculate GCF of 1300,2296
| 2 | 1300, 2296 |
| 2 | 650, 1148 |
| 325, 574 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 1300,2296 By Matching Biggest Common Factor Method
Now, list down the factors of 1300
:1,2,4,5,10,13,20,25,26,50,52,65,100,130,260,325,650,1300
Now, list down the factors of 2296
:1,2,4,7,8,14,28,41,56,82,164,287,328,574,1148,2296
Greatest Common Factor
We found the factors 1300,2296 . The biggest common factor number is the GCF number.
So the greatest common factor 1300,2296 is 4.
Lets's calculate LCM of 872,2656
| 2 | 872, 2656 |
| 2 | 436, 1328 |
| 2 | 218, 664 |
| 109, 332 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 109 x 332 = 289504
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/289504
Therefore, the GCF of Fractions 1300/872,2296/2656 is 4/289504
Least Common Multiple of 872,2656 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 872,2656 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(872,2656) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(872,2656) x common factors =8 x 1 = 8
LCM(872,2656) = ( 872 × 2656 ) / 8
LCM(872,2656) = 2316032 / 8
LCM(872,2656) = 289504
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FAQs on GCF of Fractions of 1300/872, 2296/2656
1. What is the HCF of 1300,2296?
The HCF of 1300,2296 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 1300/872, 2296/2656?
Answer: GCF of Numerators as per given numbers 1300/872, 2296/2656 is
GCF of Numerators i.e. for 1300,2296 is 4
LCM of denominators i.e. for 872,2656 is 289504.
Thus, GCF of Fractions is 4/289504.Finally, GCF of Fractions for 1300/872, 2296/2656 is 4/289504.