Use our free GCF of Fractions Calculator tool to compute the GCF of 65/102, 84/294, 417/120 i.e 1/99960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 65/102, 84/294, 417/120.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 65/102,84/294,417/120
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 65/102,84/294,417/120, numerators are 65,84,417
Denominators are 102,294,120
The GCF of 65,84,417 is 1 .
LCM of 102,294,120 is 99960.
The greatest common factor of 65/102,84/294,417/120 = [GCF of 65,84,417]/[LCM of 102,294,120]= 1/99960
Therefore, the GCF of 65/102,84/294,417/120 is 1/99960.
To find the highest common factor of 65,84,417, we have to find the factors of both numbers and list the highest common factor.
The factors of 65 are 1, 5, 13, 65
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 417 are 1, 3, 139, 417
The HCF of 65,84,417 is 1.
Lets's calculate GCF of 65,84,417
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 65
:1,5,13,65
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 417
:1,3,139,417
Greatest Common Factor
We found the factors 65,84,417 . The biggest common factor number is the GCF number.
So the greatest common factor 65,84,417 is 1.
Lets's calculate LCM of 102,294,120
2 | 102, 294, 120 |
3 | 51, 147, 60 |
17, 49, 20 |
∴ So the LCM of the given numbers is 2 x 3 x 17 x 49 x 20 = 99960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/99960
Therefore, the GCF of Fractions 65/102,84/294,417/120 is 1/99960
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 102,294,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(102,294,120) = 6
common factors(in case of two or more numbers have common factors) = 6
GCF(102,294,120) x common factors =6 x 6 = 36
LCM(102,294,120) = ( 102 × 294 × 120 ) / 36
LCM(102,294,120) = 3598560 / 36
LCM(102,294,120) = 99960
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 65,84,417?
The HCF of 65,84,417 is 1
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 65/102, 84/294, 417/120?
Answer: GCF of Numerators as per given numbers 65/102, 84/294, 417/120 is
GCF of Numerators i.e. for 65,84,417 is 1
LCM of denominators i.e. for 102,294,120 is 99960.
Thus, GCF of Fractions is 1/99960.Finally, GCF of Fractions for 65/102, 84/294, 417/120 is 1/99960.