Use our free GCF of Fractions Calculator tool to compute the GCF of 410/217, 984/661 i.e 82/143437 easily. The following is the detailed procedure to determine the greatest common factor of fractions 410/217, 984/661.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 410/217,984/661
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 410/217,984/661, numerators are 410,984
Denominators are 217,661
The GCF of 410,984 is 82 .
LCM of 217,661 is 143437.
The greatest common factor of 410/217,984/661 = [GCF of 410,984]/[LCM of 217,661]= 82/143437
Therefore, the GCF of 410/217,984/661 is 82/143437.
To find the highest common factor of 410,984, we have to find the factors of both numbers and list the highest common factor.
The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410
The factors of 984 are 1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984
The HCF of 410,984 is 82.
Lets's calculate GCF of 410,984
2 | 410, 984 |
41 | 205, 492 |
5, 12 |
∴ So the GCF of the given numbers is 2 x 41 = 82
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Now, list down the factors of 984
:1,2,3,4,6,8,12,24,41,82,123,164,246,328,492,984
Greatest Common Factor
We found the factors 410,984 . The biggest common factor number is the GCF number.
So the greatest common factor 410,984 is 82.
Lets's calculate LCM of 217,661
Given numbers has no common factors except 1. So, there LCM is their product i.e 143437
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 82/143437
Therefore, the GCF of Fractions 410/217,984/661 is 82/143437
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 217,661 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(217,661) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(217,661) x common factors =1 x 1 = 1
LCM(217,661) = ( 217 × 661 ) / 1
LCM(217,661) = 143437 / 1
LCM(217,661) = 143437
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 410,984?
The HCF of 410,984 is 82
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 410/217, 984/661?
Answer: GCF of Numerators as per given numbers 410/217, 984/661 is
GCF of Numerators i.e. for 410,984 is 82
LCM of denominators i.e. for 217,661 is 143437.
Thus, GCF of Fractions is 82/143437.Finally, GCF of Fractions for 410/217, 984/661 is 82/143437.