Use our free GCF of Fractions Calculator tool to compute the GCF of 51/284, 23/322, 714/800 i.e 1/9144800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 51/284, 23/322, 714/800.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 51/284,23/322,714/800
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 51/284,23/322,714/800, numerators are 51,23,714
Denominators are 284,322,800
The GCF of 51,23,714 is 1 .
LCM of 284,322,800 is 9144800.
The greatest common factor of 51/284,23/322,714/800 = [GCF of 51,23,714]/[LCM of 284,322,800]= 1/9144800
Therefore, the GCF of 51/284,23/322,714/800 is 1/9144800.
To find the highest common factor of 51,23,714, we have to find the factors of both numbers and list the highest common factor.
The factors of 51 are 1, 3, 17, 51
The factors of 23 are 1, 23
The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
The HCF of 51,23,714 is 1.
Lets's calculate GCF of 51,23,714
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 51
:1,3,17,51
Now, list down the factors of 23
:1,23
Now, list down the factors of 714
:1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714
Greatest Common Factor
We found the factors 51,23,714 . The biggest common factor number is the GCF number.
So the greatest common factor 51,23,714 is 1.
Lets's calculate LCM of 284,322,800
2 | 284, 322, 800 |
2 | 142, 161, 400 |
71, 161, 200 |
∴ So the LCM of the given numbers is 2 x 2 x 71 x 161 x 200 = 9144800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9144800
Therefore, the GCF of Fractions 51/284,23/322,714/800 is 1/9144800
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 284,322,800 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(284,322,800) = 2
common factors(in case of two or more numbers have common factors) = 4
GCF(284,322,800) x common factors =2 x 4 = 8
LCM(284,322,800) = ( 284 × 322 × 800 ) / 8
LCM(284,322,800) = 73158400 / 8
LCM(284,322,800) = 9144800
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 51,23,714?
The HCF of 51,23,714 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 51/284, 23/322, 714/800?
Answer: GCF of Numerators as per given numbers 51/284, 23/322, 714/800 is
GCF of Numerators i.e. for 51,23,714 is 1
LCM of denominators i.e. for 284,322,800 is 9144800.
Thus, GCF of Fractions is 1/9144800.Finally, GCF of Fractions for 51/284, 23/322, 714/800 is 1/9144800.