Use our free GCF of Fractions Calculator tool to compute the GCF of 366/689, 414/315 i.e 6/217035 easily. The following is the detailed procedure to determine the greatest common factor of fractions 366/689, 414/315.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 366/689,414/315
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 366/689,414/315, numerators are 366,414
Denominators are 689,315
The GCF of 366,414 is 6 .
LCM of 689,315 is 217035.
The greatest common factor of 366/689,414/315 = [GCF of 366,414]/[LCM of 689,315]= 6/217035
Therefore, the GCF of 366/689,414/315 is 6/217035.
To find the highest common factor of 366,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 366 are 1, 2, 3, 6, 61, 122, 183, 366
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 366,414 is 6.
Lets's calculate GCF of 366,414
2 | 366, 414 |
3 | 183, 207 |
61, 69 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 366
:1,2,3,6,61,122,183,366
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 366,414 . The biggest common factor number is the GCF number.
So the greatest common factor 366,414 is 6.
Lets's calculate LCM of 689,315
Given numbers has no common factors except 1. So, there LCM is their product i.e 217035
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/217035
Therefore, the GCF of Fractions 366/689,414/315 is 6/217035
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 689,315 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(689,315) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(689,315) x common factors =1 x 1 = 1
LCM(689,315) = ( 689 × 315 ) / 1
LCM(689,315) = 217035 / 1
LCM(689,315) = 217035
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 366,414?
The HCF of 366,414 is 6
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 366/689, 414/315?
Answer: GCF of Numerators as per given numbers 366/689, 414/315 is
GCF of Numerators i.e. for 366,414 is 6
LCM of denominators i.e. for 689,315 is 217035.
Thus, GCF of Fractions is 6/217035.Finally, GCF of Fractions for 366/689, 414/315 is 6/217035.