GCF of 2600/329, 9724/6514
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2600/329, 9724/6514 i.e 52/2143106 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2600/329, 9724/6514.
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 2600/329,9724/6514?
Given fractions are 2600/329,9724/6514
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 2600/329,9724/6514, numerators are 2600,9724
Denominators are 329,6514
The GCF of 2600,9724 is 52 .
LCM of 329,6514 is 2143106.
The greatest common factor of 2600/329,9724/6514 = [GCF of 2600,9724]/[LCM of 329,6514]= 52/2143106
Therefore, the GCF of 2600/329,9724/6514 is 52/2143106.
To find the highest common factor of 2600,9724, we have to find the factors of both numbers and list the highest common factor.
The factors of 2600 are 1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 130, 200, 260, 325, 520, 650, 1300, 2600
The factors of 9724 are 1, 2, 4, 11, 13, 17, 22, 26, 34, 44, 52, 68, 143, 187, 221, 286, 374, 442, 572, 748, 884, 2431, 4862, 9724
The HCF of 2600,9724 is 52.
Lets's calculate GCF of 2600,9724
| 2 | 2600, 9724 |
| 2 | 1300, 4862 |
| 13 | 650, 2431 |
| 50, 187 |
∴ So the GCF of the given numbers is 2 x 2 x 13 = 52
Greatest Common Factor of 2600,9724 By Matching Biggest Common Factor Method
Now, list down the factors of 2600
:1,2,4,5,8,10,13,20,25,26,40,50,52,65,100,104,130,200,260,325,520,650,1300,2600
Now, list down the factors of 9724
:1,2,4,11,13,17,22,26,34,44,52,68,143,187,221,286,374,442,572,748,884,2431,4862,9724
Greatest Common Factor
We found the factors 2600,9724 . The biggest common factor number is the GCF number.
So the greatest common factor 2600,9724 is 52.
Lets's calculate LCM of 329,6514
Given numbers has no common factors except 1. So, there LCM is their product i.e 2143106
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 52/2143106
Therefore, the GCF of Fractions 2600/329,9724/6514 is 52/2143106
Least Common Multiple of 329,6514 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 329,6514 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(329,6514) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(329,6514) x common factors =1 x 1 = 1
LCM(329,6514) = ( 329 × 6514 ) / 1
LCM(329,6514) = 2143106 / 1
LCM(329,6514) = 2143106
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FAQs on GCF of Fractions of 2600/329, 9724/6514
1. What is the HCF of 2600,9724?
The HCF of 2600,9724 is 52
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 2600/329, 9724/6514?
Answer: GCF of Numerators as per given numbers 2600/329, 9724/6514 is
GCF of Numerators i.e. for 2600,9724 is 52
LCM of denominators i.e. for 329,6514 is 2143106.
Thus, GCF of Fractions is 52/2143106.Finally, GCF of Fractions for 2600/329, 9724/6514 is 52/2143106.