GCF of 7284/784, 5640/535
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7284/784, 5640/535 i.e 12/419440 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7284/784, 5640/535.
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 7284/784,5640/535?
Given fractions are 7284/784,5640/535
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 7284/784,5640/535, numerators are 7284,5640
Denominators are 784,535
The GCF of 7284,5640 is 12 .
LCM of 784,535 is 419440.
The greatest common factor of 7284/784,5640/535 = [GCF of 7284,5640]/[LCM of 784,535]= 12/419440
Therefore, the GCF of 7284/784,5640/535 is 12/419440.
To find the highest common factor of 7284,5640, we have to find the factors of both numbers and list the highest common factor.
The factors of 7284 are 1, 2, 3, 4, 6, 12, 607, 1214, 1821, 2428, 3642, 7284
The factors of 5640 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 47, 60, 94, 120, 141, 188, 235, 282, 376, 470, 564, 705, 940, 1128, 1410, 1880, 2820, 5640
The HCF of 7284,5640 is 12.
Lets's calculate GCF of 7284,5640
| 2 | 7284, 5640 |
| 2 | 3642, 2820 |
| 3 | 1821, 1410 |
| 607, 470 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 7284,5640 By Matching Biggest Common Factor Method
Now, list down the factors of 7284
:1,2,3,4,6,12,607,1214,1821,2428,3642,7284
Now, list down the factors of 5640
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,47,60,94,120,141,188,235,282,376,470,564,705,940,1128,1410,1880,2820,5640
Greatest Common Factor
We found the factors 7284,5640 . The biggest common factor number is the GCF number.
So the greatest common factor 7284,5640 is 12.
Lets's calculate LCM of 784,535
Given numbers has no common factors except 1. So, there LCM is their product i.e 419440
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/419440
Therefore, the GCF of Fractions 7284/784,5640/535 is 12/419440
Least Common Multiple of 784,535 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 784,535 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(784,535) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(784,535) x common factors =1 x 1 = 1
LCM(784,535) = ( 784 × 535 ) / 1
LCM(784,535) = 419440 / 1
LCM(784,535) = 419440
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FAQs on GCF of Fractions of 7284/784, 5640/535
1. What is the HCF of 7284,5640?
The HCF of 7284,5640 is 12
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 7284/784, 5640/535?
Answer: GCF of Numerators as per given numbers 7284/784, 5640/535 is
GCF of Numerators i.e. for 7284,5640 is 12
LCM of denominators i.e. for 784,535 is 419440.
Thus, GCF of Fractions is 12/419440.Finally, GCF of Fractions for 7284/784, 5640/535 is 12/419440.