GCF of 399/484, 5200/314
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 399/484, 5200/314 i.e 1/75988 easily. The following is the detailed procedure to determine the greatest common factor of fractions 399/484, 5200/314.
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 399/484,5200/314?
Given fractions are 399/484,5200/314
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 399/484,5200/314, numerators are 399,5200
Denominators are 484,314
The GCF of 399,5200 is 1 .
LCM of 484,314 is 75988.
The greatest common factor of 399/484,5200/314 = [GCF of 399,5200]/[LCM of 484,314]= 1/75988
Therefore, the GCF of 399/484,5200/314 is 1/75988.
To find the highest common factor of 399,5200, we have to find the factors of both numbers and list the highest common factor.
The factors of 399 are 1, 3, 7, 19, 21, 57, 133, 399
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 399,5200 is 1.
Lets's calculate GCF of 399,5200
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 399,5200 By Matching Biggest Common Factor Method
Now, list down the factors of 399
:1,3,7,19,21,57,133,399
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 399,5200 . The biggest common factor number is the GCF number.
So the greatest common factor 399,5200 is 1.
Lets's calculate LCM of 484,314
| 2 | 484, 314 |
| 242, 157 |
∴ So the LCM of the given numbers is 2 x 242 x 157 = 75988
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/75988
Therefore, the GCF of Fractions 399/484,5200/314 is 1/75988
Least Common Multiple of 484,314 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 484,314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(484,314) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(484,314) x common factors =2 x 1 = 2
LCM(484,314) = ( 484 × 314 ) / 2
LCM(484,314) = 151976 / 2
LCM(484,314) = 75988
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FAQs on GCF of Fractions of 399/484, 5200/314
1. What is the HCF of 399,5200?
The HCF of 399,5200 is 1
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 399/484, 5200/314?
Answer: GCF of Numerators as per given numbers 399/484, 5200/314 is
GCF of Numerators i.e. for 399,5200 is 1
LCM of denominators i.e. for 484,314 is 75988.
Thus, GCF of Fractions is 1/75988.Finally, GCF of Fractions for 399/484, 5200/314 is 1/75988.