Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 28/74,75/25,31/37,321/21
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 28,75,31,321
Greatest Common Factor of Numerators i.e. GCF of 28,75,31,321 is 1 .
LCM of Denominators means LCM of 74,25,37,21 as per the given fractions.
LCM of 74,25,37,21 is 38850 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 28,75,31,321
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 28
List of positive integer factors of 28 that divides 28 without a remainder.
1,2,4,7,14,28
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Factors of 31
List of positive integer factors of 31 that divides 31 without a remainder.
1,31
Factors of 321
List of positive integer factors of 321 that divides 321 without a remainder.
1,3,107,321
Greatest Common Factor
We found the factors 28,75,31,321 . The biggest common factor number is the GCF number.
So the greatest common factor 28,75,31,321 is 1.
Lets's calculate LCM of 74,25,37,21
37 | 74, 25, 37, 21 |
2, 25, 1, 21 |
∴ So the LCM of the given numbers is 37 x 2 x 25 x 1 x 21 = 38850
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/38850
Therefore, the GCF of Fractions 28/74,75/25,31/37,321/21 is 1/38850
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 74,25,37,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,25,37,21) = 1
common factors(in case of two or more numbers have common factors) = 37
GCF(74,25,37,21) x common factors =1 x 37 = 37
LCM(74,25,37,21) = ( 74 × 25 × 37 × 21 ) / 37
LCM(74,25,37,21) = 1437450 / 37
LCM(74,25,37,21) = 38850
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 28/74, 75/25, 31/37, 321/21?
Answer: GCF of Numerators as per given numbers 28/74, 75/25, 31/37, 321/21 is
GCF of Numerators i.e. for 28,75,31,321 is 1
LCM of denominators i.e. for 74,25,37,21 is 38850.
Thus, GCF of Fractions is 1/38850.Finally, GCF of Fractions for 28/74, 75/25, 31/37, 321/21 is 1/38850.