Use our free GCF of Fractions Calculator tool to compute the GCF of 21/57, 994/31, 113/857 i.e 1/1514319 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/57, 994/31, 113/857.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 21/57,994/31,113/857
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 21/57,994/31,113/857, numerators are 21,994,113
Denominators are 57,31,857
The GCF of 21,994,113 is 1 .
LCM of 57,31,857 is 1514319.
The greatest common factor of 21/57,994/31,113/857 = [GCF of 21,994,113]/[LCM of 57,31,857]= 1/1514319
Therefore, the GCF of 21/57,994/31,113/857 is 1/1514319.
To find the highest common factor of 21,994,113, we have to find the factors of both numbers and list the highest common factor.
The factors of 21 are 1, 3, 7, 21
The factors of 994 are 1, 2, 7, 14, 71, 142, 497, 994
The factors of 113 are 1, 113
The HCF of 21,994,113 is 1.
Lets's calculate GCF of 21,994,113
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 994
:1,2,7,14,71,142,497,994
Now, list down the factors of 113
:1,113
Greatest Common Factor
We found the factors 21,994,113 . The biggest common factor number is the GCF number.
So the greatest common factor 21,994,113 is 1.
Lets's calculate LCM of 57,31,857
Given numbers has no common factors except 1. So, there LCM is their product i.e 1514319
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1514319
Therefore, the GCF of Fractions 21/57,994/31,113/857 is 1/1514319
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 57,31,857 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(57,31,857) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(57,31,857) x common factors =1 x 1 = 1
LCM(57,31,857) = ( 57 × 31 × 857 ) / 1
LCM(57,31,857) = 1514319 / 1
LCM(57,31,857) = 1514319
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 21,994,113?
The HCF of 21,994,113 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 21/57, 994/31, 113/857?
Answer: GCF of Numerators as per given numbers 21/57, 994/31, 113/857 is
GCF of Numerators i.e. for 21,994,113 is 1
LCM of denominators i.e. for 57,31,857 is 1514319.
Thus, GCF of Fractions is 1/1514319.Finally, GCF of Fractions for 21/57, 994/31, 113/857 is 1/1514319.