GCF of 5664/512, 8280/9145
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5664/512, 8280/9145 i.e 24/4682240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5664/512, 8280/9145.
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 5664/512,8280/9145?
Given fractions are 5664/512,8280/9145
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 5664/512,8280/9145, numerators are 5664,8280
Denominators are 512,9145
The GCF of 5664,8280 is 24 .
LCM of 512,9145 is 4682240.
The greatest common factor of 5664/512,8280/9145 = [GCF of 5664,8280]/[LCM of 512,9145]= 24/4682240
Therefore, the GCF of 5664/512,8280/9145 is 24/4682240.
To find the highest common factor of 5664,8280, we have to find the factors of both numbers and list the highest common factor.
The factors of 5664 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 59, 96, 118, 177, 236, 354, 472, 708, 944, 1416, 1888, 2832, 5664
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 HCF of 5664,8280 is 24.
Lets's calculate GCF of 5664,8280
| 2 | 5664, 8280 |
| 2 | 2832, 4140 |
| 2 | 1416, 2070 |
| 3 | 708, 1035 |
| 236, 345 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
Greatest Common Factor of 5664,8280 By Matching Biggest Common Factor Method
Now, list down the factors of 5664
:1,2,3,4,6,8,12,16,24,32,48,59,96,118,177,236,354,472,708,944,1416,1888,2832,5664
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
Greatest Common Factor
We found the factors 5664,8280 . The biggest common factor number is the GCF number.
So the greatest common factor 5664,8280 is 24.
Lets's calculate LCM of 512,9145
Given numbers has no common factors except 1. So, there LCM is their product i.e 4682240
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/4682240
Therefore, the GCF of Fractions 5664/512,8280/9145 is 24/4682240
Least Common Multiple of 512,9145 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 512,9145 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(512,9145) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(512,9145) x common factors =1 x 1 = 1
LCM(512,9145) = ( 512 × 9145 ) / 1
LCM(512,9145) = 4682240 / 1
LCM(512,9145) = 4682240
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FAQs on GCF of Fractions of 5664/512, 8280/9145
1. What is the HCF of 5664,8280?
The HCF of 5664,8280 is 24
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 5664/512, 8280/9145?
Answer: GCF of Numerators as per given numbers 5664/512, 8280/9145 is
GCF of Numerators i.e. for 5664,8280 is 24
LCM of denominators i.e. for 512,9145 is 4682240.
Thus, GCF of Fractions is 24/4682240.Finally, GCF of Fractions for 5664/512, 8280/9145 is 24/4682240.