Use our free GCF of Fractions Calculator tool to compute the GCF of 284/689, 300/208 i.e 4/11024 easily. The following is the detailed procedure to determine the greatest common factor of fractions 284/689, 300/208.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 284/689,300/208
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 284/689,300/208, numerators are 284,300
Denominators are 689,208
The GCF of 284,300 is 4 .
LCM of 689,208 is 11024.
The greatest common factor of 284/689,300/208 = [GCF of 284,300]/[LCM of 689,208]= 4/11024
Therefore, the GCF of 284/689,300/208 is 4/11024.
To find the highest common factor of 284,300, we have to find the factors of both numbers and list the highest common factor.
The factors of 284 are 1, 2, 4, 71, 142, 284
The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
The HCF of 284,300 is 4.
Lets's calculate GCF of 284,300
2 | 284, 300 |
2 | 142, 150 |
71, 75 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 284
:1,2,4,71,142,284
Now, list down the factors of 300
:1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300
Greatest Common Factor
We found the factors 284,300 . The biggest common factor number is the GCF number.
So the greatest common factor 284,300 is 4.
Lets's calculate LCM of 689,208
13 | 689, 208 |
53, 16 |
∴ So the LCM of the given numbers is 13 x 53 x 16 = 11024
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/11024
Therefore, the GCF of Fractions 284/689,300/208 is 4/11024
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 689,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(689,208) = 13
common factors(in case of two or more numbers have common factors) = 1
GCF(689,208) x common factors =13 x 1 = 13
LCM(689,208) = ( 689 × 208 ) / 13
LCM(689,208) = 143312 / 13
LCM(689,208) = 11024
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 284,300?
The HCF of 284,300 is 4
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 284/689, 300/208?
Answer: GCF of Numerators as per given numbers 284/689, 300/208 is
GCF of Numerators i.e. for 284,300 is 4
LCM of denominators i.e. for 689,208 is 11024.
Thus, GCF of Fractions is 4/11024.Finally, GCF of Fractions for 284/689, 300/208 is 4/11024.