Use our free GCF of Fractions Calculator tool to compute the GCF of 336/705, 300/108 i.e 12/25380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 336/705, 300/108.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 336/705,300/108
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 336/705,300/108, numerators are 336,300
Denominators are 705,108
The GCF of 336,300 is 12 .
LCM of 705,108 is 25380.
The greatest common factor of 336/705,300/108 = [GCF of 336,300]/[LCM of 705,108]= 12/25380
Therefore, the GCF of 336/705,300/108 is 12/25380.
To find the highest common factor of 336,300, we have to find the factors of both numbers and list the highest common factor.
The factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336
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 336,300 is 12.
Lets's calculate GCF of 336,300
2 | 336, 300 |
2 | 168, 150 |
3 | 84, 75 |
28, 25 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Now, list down the factors of 336
:1,2,3,4,6,7,8,12,14,16,21,24,28,42,48,56,84,112,168,336
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 336,300 . The biggest common factor number is the GCF number.
So the greatest common factor 336,300 is 12.
Lets's calculate LCM of 705,108
3 | 705, 108 |
235, 36 |
∴ So the LCM of the given numbers is 3 x 235 x 36 = 25380
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/25380
Therefore, the GCF of Fractions 336/705,300/108 is 12/25380
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 705,108 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(705,108) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(705,108) x common factors =3 x 1 = 3
LCM(705,108) = ( 705 × 108 ) / 3
LCM(705,108) = 76140 / 3
LCM(705,108) = 25380
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 336,300?
The HCF of 336,300 is 12
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 336/705, 300/108?
Answer: GCF of Numerators as per given numbers 336/705, 300/108 is
GCF of Numerators i.e. for 336,300 is 12
LCM of denominators i.e. for 705,108 is 25380.
Thus, GCF of Fractions is 12/25380.Finally, GCF of Fractions for 336/705, 300/108 is 12/25380.