GCF of 3728/72, 5200/399
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3728/72, 5200/399 i.e 16/9576 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3728/72, 5200/399.
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 3728/72,5200/399?
Given fractions are 3728/72,5200/399
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 3728/72,5200/399, numerators are 3728,5200
Denominators are 72,399
The GCF of 3728,5200 is 16 .
LCM of 72,399 is 9576.
The greatest common factor of 3728/72,5200/399 = [GCF of 3728,5200]/[LCM of 72,399]= 16/9576
Therefore, the GCF of 3728/72,5200/399 is 16/9576.
To find the highest common factor of 3728,5200, we have to find the factors of both numbers and list the highest common factor.
The factors of 3728 are 1, 2, 4, 8, 16, 233, 466, 932, 1864, 3728
The factors of 5200 are 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 40, 50, 52, 65, 80, 100, 104, 130, 200, 208, 260, 325, 400, 520, 650, 1040, 1300, 2600, 5200
The HCF of 3728,5200 is 16.
Lets's calculate GCF of 3728,5200
| 2 | 3728, 5200 |
| 2 | 1864, 2600 |
| 2 | 932, 1300 |
| 2 | 466, 650 |
| 233, 325 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 3728,5200 By Matching Biggest Common Factor Method
Now, list down the factors of 3728
:1,2,4,8,16,233,466,932,1864,3728
Now, list down the factors of 5200
:1,2,4,5,8,10,13,16,20,25,26,40,50,52,65,80,100,104,130,200,208,260,325,400,520,650,1040,1300,2600,5200
Greatest Common Factor
We found the factors 3728,5200 . The biggest common factor number is the GCF number.
So the greatest common factor 3728,5200 is 16.
Lets's calculate LCM of 72,399
| 3 | 72, 399 |
| 24, 133 |
∴ So the LCM of the given numbers is 3 x 24 x 133 = 9576
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/9576
Therefore, the GCF of Fractions 3728/72,5200/399 is 16/9576
Least Common Multiple of 72,399 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 72,399 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(72,399) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(72,399) x common factors =3 x 1 = 3
LCM(72,399) = ( 72 × 399 ) / 3
LCM(72,399) = 28728 / 3
LCM(72,399) = 9576
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FAQs on GCF of Fractions of 3728/72, 5200/399
1. What is the HCF of 3728,5200?
The HCF of 3728,5200 is 16
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 3728/72, 5200/399?
Answer: GCF of Numerators as per given numbers 3728/72, 5200/399 is
GCF of Numerators i.e. for 3728,5200 is 16
LCM of denominators i.e. for 72,399 is 9576.
Thus, GCF of Fractions is 16/9576.Finally, GCF of Fractions for 3728/72, 5200/399 is 16/9576.