GCF of 559/48, 286/400
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 559/48, 286/400 i.e 13/1200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 559/48, 286/400.
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 559/48,286/400?
Given fractions are 559/48,286/400
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 559/48,286/400, numerators are 559,286
Denominators are 48,400
The GCF of 559,286 is 13 .
LCM of 48,400 is 1200.
The greatest common factor of 559/48,286/400 = [GCF of 559,286]/[LCM of 48,400]= 13/1200
Therefore, the GCF of 559/48,286/400 is 13/1200.
To find the highest common factor of 559,286, we have to find the factors of both numbers and list the highest common factor.
The factors of 559 are 1, 13, 43, 559
The factors of 286 are 1, 2, 11, 13, 22, 26, 143, 286
The HCF of 559,286 is 13.
Lets's calculate GCF of 559,286
| 13 | 559, 286 |
| 43, 22 |
∴ So the GCF of the given numbers is 13 = 13
Greatest Common Factor of 559,286 By Matching Biggest Common Factor Method
Now, list down the factors of 559
:1,13,43,559
Now, list down the factors of 286
:1,2,11,13,22,26,143,286
Greatest Common Factor
We found the factors 559,286 . The biggest common factor number is the GCF number.
So the greatest common factor 559,286 is 13.
Lets's calculate LCM of 48,400
| 2 | 48, 400 |
| 2 | 24, 200 |
| 2 | 12, 100 |
| 2 | 6, 50 |
| 3, 25 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 25 = 1200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/1200
Therefore, the GCF of Fractions 559/48,286/400 is 13/1200
Least Common Multiple of 48,400 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 48,400 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(48,400) = 16
common factors(in case of two or more numbers have common factors) = 1
GCF(48,400) x common factors =16 x 1 = 16
LCM(48,400) = ( 48 × 400 ) / 16
LCM(48,400) = 19200 / 16
LCM(48,400) = 1200
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FAQs on GCF of Fractions of 559/48, 286/400
1. What is the HCF of 559,286?
The HCF of 559,286 is 13
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 559/48, 286/400?
Answer: GCF of Numerators as per given numbers 559/48, 286/400 is
GCF of Numerators i.e. for 559,286 is 13
LCM of denominators i.e. for 48,400 is 1200.
Thus, GCF of Fractions is 13/1200.Finally, GCF of Fractions for 559/48, 286/400 is 13/1200.