Use our free GCF of Fractions Calculator tool to compute the GCF of 17/61, 390/46, 217/142 i.e 1/199226 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/61, 390/46, 217/142.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 17/61,390/46,217/142
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 17/61,390/46,217/142, numerators are 17,390,217
Denominators are 61,46,142
The GCF of 17,390,217 is 1 .
LCM of 61,46,142 is 199226.
The greatest common factor of 17/61,390/46,217/142 = [GCF of 17,390,217]/[LCM of 61,46,142]= 1/199226
Therefore, the GCF of 17/61,390/46,217/142 is 1/199226.
To find the highest common factor of 17,390,217, we have to find the factors of both numbers and list the highest common factor.
The factors of 17 are 1, 17
The factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390
The factors of 217 are 1, 7, 31, 217
The HCF of 17,390,217 is 1.
Lets's calculate GCF of 17,390,217
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 17
:1,17
Now, list down the factors of 390
:1,2,3,5,6,10,13,15,26,30,39,65,78,130,195,390
Now, list down the factors of 217
:1,7,31,217
Greatest Common Factor
We found the factors 17,390,217 . The biggest common factor number is the GCF number.
So the greatest common factor 17,390,217 is 1.
Lets's calculate LCM of 61,46,142
2 | 61, 46, 142 |
61, 23, 71 |
∴ So the LCM of the given numbers is 2 x 61 x 23 x 71 = 199226
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/199226
Therefore, the GCF of Fractions 17/61,390/46,217/142 is 1/199226
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 61,46,142 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(61,46,142) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(61,46,142) x common factors =1 x 2 = 2
LCM(61,46,142) = ( 61 × 46 × 142 ) / 2
LCM(61,46,142) = 398452 / 2
LCM(61,46,142) = 199226
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 17,390,217?
The HCF of 17,390,217 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 17/61, 390/46, 217/142?
Answer: GCF of Numerators as per given numbers 17/61, 390/46, 217/142 is
GCF of Numerators i.e. for 17,390,217 is 1
LCM of denominators i.e. for 61,46,142 is 199226.
Thus, GCF of Fractions is 1/199226.Finally, GCF of Fractions for 17/61, 390/46, 217/142 is 1/199226.