Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 71/31,59/17,16/41,76/17
Formula to find GCF of Fractions is
GCF = GCF of Numerators/LCM of Denominators
As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators
In the given fractions GCF of Numerators means GCF of 71,59,16,76
Greatest Common Factor of Numerators i.e. GCF of 71,59,16,76 is 1 .
LCM of Denominators means LCM of 31,17,41,17 as per the given fractions.
LCM of 31,17,41,17 is 21607 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 71,59,16,76
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 71
List of positive integer factors of 71 that divides 71 without a remainder.
1,71
Factors of 59
List of positive integer factors of 59 that divides 59 without a remainder.
1,59
Factors of 16
List of positive integer factors of 16 that divides 16 without a remainder.
1,2,4,8,16
Factors of 76
List of positive integer factors of 76 that divides 76 without a remainder.
1,2,4,19,38,76
Greatest Common Factor
We found the factors 71,59,16,76 . The biggest common factor number is the GCF number.
So the greatest common factor 71,59,16,76 is 1.
Lets's calculate LCM of 31,17,41,17
17 | 31, 17, 41, 17 |
31, 1, 41, 1 |
∴ So the LCM of the given numbers is 17 x 31 x 1 x 41 x 1 = 21607
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/21607
Therefore, the GCF of Fractions 71/31,59/17,16/41,76/17 is 1/21607
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 31,17,41,17 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,17,41,17) = 1
common factors(in case of two or more numbers have common factors) = 17
GCF(31,17,41,17) x common factors =1 x 17 = 17
LCM(31,17,41,17) = ( 31 × 17 × 41 × 17 ) / 17
LCM(31,17,41,17) = 367319 / 17
LCM(31,17,41,17) = 21607
Here are some samples of GCF of Fractions calculations.
Here are some samples of GCF of Fractions calculations.
1. 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.
2. What is the GCF of Fractions for 71/31, 59/17, 16/41, 76/17?
Answer: GCF of Numerators as per given numbers 71/31, 59/17, 16/41, 76/17 is
GCF of Numerators i.e. for 71,59,16,76 is 1
LCM of denominators i.e. for 31,17,41,17 is 21607.
Thus, GCF of Fractions is 1/21607.Finally, GCF of Fractions for 71/31, 59/17, 16/41, 76/17 is 1/21607.