Use our free GCF of Fractions Calculator tool to compute the GCF of 636/666, 723/778 i.e 3/259074 easily. The following is the detailed procedure to determine the greatest common factor of fractions 636/666, 723/778.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 636/666,723/778
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 636/666,723/778, numerators are 636,723
Denominators are 666,778
The GCF of 636,723 is 3 .
LCM of 666,778 is 259074.
The greatest common factor of 636/666,723/778 = [GCF of 636,723]/[LCM of 666,778]= 3/259074
Therefore, the GCF of 636/666,723/778 is 3/259074.
To find the highest common factor of 636,723, we have to find the factors of both numbers and list the highest common factor.
The factors of 636 are 1, 2, 3, 4, 6, 12, 53, 106, 159, 212, 318, 636
The factors of 723 are 1, 3, 241, 723
The HCF of 636,723 is 3.
Lets's calculate GCF of 636,723
3 | 636, 723 |
212, 241 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 636
:1,2,3,4,6,12,53,106,159,212,318,636
Now, list down the factors of 723
:1,3,241,723
Greatest Common Factor
We found the factors 636,723 . The biggest common factor number is the GCF number.
So the greatest common factor 636,723 is 3.
Lets's calculate LCM of 666,778
2 | 666, 778 |
333, 389 |
∴ So the LCM of the given numbers is 2 x 333 x 389 = 259074
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/259074
Therefore, the GCF of Fractions 636/666,723/778 is 3/259074
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 666,778 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(666,778) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(666,778) x common factors =2 x 1 = 2
LCM(666,778) = ( 666 × 778 ) / 2
LCM(666,778) = 518148 / 2
LCM(666,778) = 259074
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 636,723?
The HCF of 636,723 is 3
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 636/666, 723/778?
Answer: GCF of Numerators as per given numbers 636/666, 723/778 is
GCF of Numerators i.e. for 636,723 is 3
LCM of denominators i.e. for 666,778 is 259074.
Thus, GCF of Fractions is 3/259074.Finally, GCF of Fractions for 636/666, 723/778 is 3/259074.