Use our free GCF of Fractions Calculator tool to compute the GCF of 800/402, 616/500 i.e 8/100500 easily. The following is the detailed procedure to determine the greatest common factor of fractions 800/402, 616/500.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 800/402,616/500
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 800/402,616/500, numerators are 800,616
Denominators are 402,500
The GCF of 800,616 is 8 .
LCM of 402,500 is 100500.
The greatest common factor of 800/402,616/500 = [GCF of 800,616]/[LCM of 402,500]= 8/100500
Therefore, the GCF of 800/402,616/500 is 8/100500.
To find the highest common factor of 800,616, we have to find the factors of both numbers and list the highest common factor.
The factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800
The factors of 616 are 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616
The HCF of 800,616 is 8.
Lets's calculate GCF of 800,616
2 | 800, 616 |
2 | 400, 308 |
2 | 200, 154 |
100, 77 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 800
:1,2,4,5,8,10,16,20,25,32,40,50,80,100,160,200,400,800
Now, list down the factors of 616
:1,2,4,7,8,11,14,22,28,44,56,77,88,154,308,616
Greatest Common Factor
We found the factors 800,616 . The biggest common factor number is the GCF number.
So the greatest common factor 800,616 is 8.
Lets's calculate LCM of 402,500
2 | 402, 500 |
201, 250 |
∴ So the LCM of the given numbers is 2 x 201 x 250 = 100500
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/100500
Therefore, the GCF of Fractions 800/402,616/500 is 8/100500
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 402,500 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(402,500) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(402,500) x common factors =2 x 1 = 2
LCM(402,500) = ( 402 × 500 ) / 2
LCM(402,500) = 201000 / 2
LCM(402,500) = 100500
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 800,616?
The HCF of 800,616 is 8
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 800/402, 616/500?
Answer: GCF of Numerators as per given numbers 800/402, 616/500 is
GCF of Numerators i.e. for 800,616 is 8
LCM of denominators i.e. for 402,500 is 100500.
Thus, GCF of Fractions is 8/100500.Finally, GCF of Fractions for 800/402, 616/500 is 8/100500.