Use our free GCF of Fractions Calculator tool to compute the GCF of 68/205, 31/719, 416/999 i.e 1/147247605 easily. The following is the detailed procedure to determine the greatest common factor of fractions 68/205, 31/719, 416/999.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 68/205,31/719,416/999
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 68/205,31/719,416/999, numerators are 68,31,416
Denominators are 205,719,999
The GCF of 68,31,416 is 1 .
LCM of 205,719,999 is 147247605.
The greatest common factor of 68/205,31/719,416/999 = [GCF of 68,31,416]/[LCM of 205,719,999]= 1/147247605
Therefore, the GCF of 68/205,31/719,416/999 is 1/147247605.
To find the highest common factor of 68,31,416, we have to find the factors of both numbers and list the highest common factor.
The factors of 68 are 1, 2, 4, 17, 34, 68
The factors of 31 are 1, 31
The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
The HCF of 68,31,416 is 1.
Lets's calculate GCF of 68,31,416
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 68
:1,2,4,17,34,68
Now, list down the factors of 31
:1,31
Now, list down the factors of 416
:1,2,4,8,13,16,26,32,52,104,208,416
Greatest Common Factor
We found the factors 68,31,416 . The biggest common factor number is the GCF number.
So the greatest common factor 68,31,416 is 1.
Lets's calculate LCM of 205,719,999
Given numbers has no common factors except 1. So, there LCM is their product i.e 147247605
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/147247605
Therefore, the GCF of Fractions 68/205,31/719,416/999 is 1/147247605
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 205,719,999 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,719,999) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(205,719,999) x common factors =1 x 1 = 1
LCM(205,719,999) = ( 205 × 719 × 999 ) / 1
LCM(205,719,999) = 147247605 / 1
LCM(205,719,999) = 147247605
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 68,31,416?
The HCF of 68,31,416 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 68/205, 31/719, 416/999?
Answer: GCF of Numerators as per given numbers 68/205, 31/719, 416/999 is
GCF of Numerators i.e. for 68,31,416 is 1
LCM of denominators i.e. for 205,719,999 is 147247605.
Thus, GCF of Fractions is 1/147247605.Finally, GCF of Fractions for 68/205, 31/719, 416/999 is 1/147247605.