Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 15/31,59/21,94/53,142/21
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 15,59,94,142
Greatest Common Factor of Numerators i.e. GCF of 15,59,94,142 is 1 .
LCM of Denominators means LCM of 31,21,53,21 as per the given fractions.
LCM of 31,21,53,21 is 34503 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 15,59,94,142
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 15
List of positive integer factors of 15 that divides 15 without a remainder.
1,3,5,15
Factors of 59
List of positive integer factors of 59 that divides 59 without a remainder.
1,59
Factors of 94
List of positive integer factors of 94 that divides 94 without a remainder.
1,2,47,94
Factors of 142
List of positive integer factors of 142 that divides 142 without a remainder.
1,2,71,142
Greatest Common Factor
We found the factors 15,59,94,142 . The biggest common factor number is the GCF number.
So the greatest common factor 15,59,94,142 is 1.
Lets's calculate LCM of 31,21,53,21
3 | 31, 21, 53, 21 |
7 | 31, 7, 53, 7 |
31, 1, 53, 1 |
∴ So the LCM of the given numbers is 3 x 7 x 31 x 1 x 53 x 1 = 34503
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/34503
Therefore, the GCF of Fractions 15/31,59/21,94/53,142/21 is 1/34503
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 31,21,53,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,21,53,21) = 1
common factors(in case of two or more numbers have common factors) = 21
GCF(31,21,53,21) x common factors =1 x 21 = 21
LCM(31,21,53,21) = ( 31 × 21 × 53 × 21 ) / 21
LCM(31,21,53,21) = 724563 / 21
LCM(31,21,53,21) = 34503
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 15/31, 59/21, 94/53, 142/21?
Answer: GCF of Numerators as per given numbers 15/31, 59/21, 94/53, 142/21 is
GCF of Numerators i.e. for 15,59,94,142 is 1
LCM of denominators i.e. for 31,21,53,21 is 34503.
Thus, GCF of Fractions is 1/34503.Finally, GCF of Fractions for 15/31, 59/21, 94/53, 142/21 is 1/34503.