GCF of 8280/903, 9765/2569
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8280/903, 9765/2569 i.e 45/331401 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8280/903, 9765/2569.
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 8280/903,9765/2569?
Given fractions are 8280/903,9765/2569
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 8280/903,9765/2569, numerators are 8280,9765
Denominators are 903,2569
The GCF of 8280,9765 is 45 .
LCM of 903,2569 is 331401.
The greatest common factor of 8280/903,9765/2569 = [GCF of 8280,9765]/[LCM of 903,2569]= 45/331401
Therefore, the GCF of 8280/903,9765/2569 is 45/331401.
To find the highest common factor of 8280,9765, we have to find the factors of both numbers and list the highest common factor.
The factors of 8280 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 23, 24, 30, 36, 40, 45, 46, 60, 69, 72, 90, 92, 115, 120, 138, 180, 184, 207, 230, 276, 345, 360, 414, 460, 552, 690, 828, 920, 1035, 1380, 1656, 2070, 2760, 4140, 8280
The factors of 9765 are 1, 3, 5, 7, 9, 15, 21, 31, 35, 45, 63, 93, 105, 155, 217, 279, 315, 465, 651, 1085, 1395, 1953, 3255, 9765
The HCF of 8280,9765 is 45.
Lets's calculate GCF of 8280,9765
| 3 | 8280, 9765 |
| 3 | 2760, 3255 |
| 5 | 920, 1085 |
| 184, 217 |
∴ So the GCF of the given numbers is 3 x 3 x 5 = 45
Greatest Common Factor of 8280,9765 By Matching Biggest Common Factor Method
Now, list down the factors of 8280
:1,2,3,4,5,6,8,9,10,12,15,18,20,23,24,30,36,40,45,46,60,69,72,90,92,115,120,138,180,184,207,230,276,345,360,414,460,552,690,828,920,1035,1380,1656,2070,2760,4140,8280
Now, list down the factors of 9765
:1,3,5,7,9,15,21,31,35,45,63,93,105,155,217,279,315,465,651,1085,1395,1953,3255,9765
Greatest Common Factor
We found the factors 8280,9765 . The biggest common factor number is the GCF number.
So the greatest common factor 8280,9765 is 45.
Lets's calculate LCM of 903,2569
| 7 | 903, 2569 |
| 129, 367 |
∴ So the LCM of the given numbers is 7 x 129 x 367 = 331401
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 45/331401
Therefore, the GCF of Fractions 8280/903,9765/2569 is 45/331401
Least Common Multiple of 903,2569 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 903,2569 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(903,2569) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(903,2569) x common factors =7 x 1 = 7
LCM(903,2569) = ( 903 × 2569 ) / 7
LCM(903,2569) = 2319807 / 7
LCM(903,2569) = 331401
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FAQs on GCF of Fractions of 8280/903, 9765/2569
1. What is the HCF of 8280,9765?
The HCF of 8280,9765 is 45
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 8280/903, 9765/2569?
Answer: GCF of Numerators as per given numbers 8280/903, 9765/2569 is
GCF of Numerators i.e. for 8280,9765 is 45
LCM of denominators i.e. for 903,2569 is 331401.
Thus, GCF of Fractions is 45/331401.Finally, GCF of Fractions for 8280/903, 9765/2569 is 45/331401.