Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 1/12,31/28,42/651,310/821
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 1,31,42,310
Greatest Common Factor of Numerators i.e. GCF of 1,31,42,310 is 1 .
LCM of Denominators means LCM of 12,28,651,821 as per the given fractions.
LCM of 12,28,651,821 is 2137884 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 1,31,42,310
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 1
List of positive integer factors of 1 that divides 1 without a remainder.
1
Factors of 31
List of positive integer factors of 31 that divides 31 without a remainder.
1,31
Factors of 42
List of positive integer factors of 42 that divides 42 without a remainder.
1,2,3,6,7,14,21,42
Factors of 310
List of positive integer factors of 310 that divides 310 without a remainder.
1,2,5,10,31,62,155,310
Greatest Common Factor
We found the factors 1,31,42,310 . The biggest common factor number is the GCF number.
So the greatest common factor 1,31,42,310 is 1.
Lets's calculate LCM of 12,28,651,821
2 | 12, 28, 651, 821 |
2 | 6, 14, 651, 821 |
3 | 3, 7, 651, 821 |
7 | 1, 7, 217, 821 |
1, 1, 31, 821 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 1 x 1 x 31 x 821 = 2137884
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2137884
Therefore, the GCF of Fractions 1/12,31/28,42/651,310/821 is 1/2137884
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 12,28,651,821 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,28,651,821) = 1
common factors(in case of two or more numbers have common factors) = 84
GCF(12,28,651,821) x common factors =1 x 84 = 84
LCM(12,28,651,821) = ( 12 × 28 × 651 × 821 ) / 84
LCM(12,28,651,821) = 179582256 / 84
LCM(12,28,651,821) = 2137884
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 1/12, 31/28, 42/651, 310/821?
Answer: GCF of Numerators as per given numbers 1/12, 31/28, 42/651, 310/821 is
GCF of Numerators i.e. for 1,31,42,310 is 1
LCM of denominators i.e. for 12,28,651,821 is 2137884.
Thus, GCF of Fractions is 1/2137884.Finally, GCF of Fractions for 1/12, 31/28, 42/651, 310/821 is 1/2137884.