GCF of 5210/214, 8300/3988
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5210/214, 8300/3988 i.e 10/426716 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5210/214, 8300/3988.
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 5210/214,8300/3988?
Given fractions are 5210/214,8300/3988
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 5210/214,8300/3988, numerators are 5210,8300
Denominators are 214,3988
The GCF of 5210,8300 is 10 .
LCM of 214,3988 is 426716.
The greatest common factor of 5210/214,8300/3988 = [GCF of 5210,8300]/[LCM of 214,3988]= 10/426716
Therefore, the GCF of 5210/214,8300/3988 is 10/426716.
To find the highest common factor of 5210,8300, we have to find the factors of both numbers and list the highest common factor.
The factors of 5210 are 1, 2, 5, 10, 521, 1042, 2605, 5210
The factors of 8300 are 1, 2, 4, 5, 10, 20, 25, 50, 83, 100, 166, 332, 415, 830, 1660, 2075, 4150, 8300
The HCF of 5210,8300 is 10.
Lets's calculate GCF of 5210,8300
| 2 | 5210, 8300 |
| 5 | 2605, 4150 |
| 521, 830 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 5210,8300 By Matching Biggest Common Factor Method
Now, list down the factors of 5210
:1,2,5,10,521,1042,2605,5210
Now, list down the factors of 8300
:1,2,4,5,10,20,25,50,83,100,166,332,415,830,1660,2075,4150,8300
Greatest Common Factor
We found the factors 5210,8300 . The biggest common factor number is the GCF number.
So the greatest common factor 5210,8300 is 10.
Lets's calculate LCM of 214,3988
| 2 | 214, 3988 |
| 107, 1994 |
∴ So the LCM of the given numbers is 2 x 107 x 1994 = 426716
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/426716
Therefore, the GCF of Fractions 5210/214,8300/3988 is 10/426716
Least Common Multiple of 214,3988 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 214,3988 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(214,3988) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(214,3988) x common factors =2 x 1 = 2
LCM(214,3988) = ( 214 × 3988 ) / 2
LCM(214,3988) = 853432 / 2
LCM(214,3988) = 426716
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FAQs on GCF of Fractions of 5210/214, 8300/3988
1. What is the HCF of 5210,8300?
The HCF of 5210,8300 is 10
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 5210/214, 8300/3988?
Answer: GCF of Numerators as per given numbers 5210/214, 8300/3988 is
GCF of Numerators i.e. for 5210,8300 is 10
LCM of denominators i.e. for 214,3988 is 426716.
Thus, GCF of Fractions is 10/426716.Finally, GCF of Fractions for 5210/214, 8300/3988 is 10/426716.