Use our free GCF of Fractions Calculator tool to compute the GCF of 366/31, 278/63, 666/63 i.e 2/1953 easily. The following is the detailed procedure to determine the greatest common factor of fractions 366/31, 278/63, 666/63.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 366/31,278/63,666/63
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 366/31,278/63,666/63, numerators are 366,278,666
Denominators are 31,63,63
The GCF of 366,278,666 is 2 .
LCM of 31,63,63 is 1953.
The greatest common factor of 366/31,278/63,666/63 = [GCF of 366,278,666]/[LCM of 31,63,63]= 2/1953
Therefore, the GCF of 366/31,278/63,666/63 is 2/1953.
To find the highest common factor of 366,278,666, we have to find the factors of both numbers and list the highest common factor.
The factors of 366 are 1, 2, 3, 6, 61, 122, 183, 366
The factors of 278 are 1, 2, 139, 278
The factors of 666 are 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666
The HCF of 366,278,666 is 2.
Lets's calculate GCF of 366,278,666
2 | 366, 278, 666 |
183, 139, 333 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 366
:1,2,3,6,61,122,183,366
Now, list down the factors of 278
:1,2,139,278
Now, list down the factors of 666
:1,2,3,6,9,18,37,74,111,222,333,666
Greatest Common Factor
We found the factors 366,278,666 . The biggest common factor number is the GCF number.
So the greatest common factor 366,278,666 is 2.
Lets's calculate LCM of 31,63,63
3 | 31, 63, 63 |
3 | 31, 21, 21 |
7 | 31, 7, 7 |
31, 1, 1 |
∴ So the LCM of the given numbers is 3 x 3 x 7 x 31 x 1 x 1 = 1953
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1953
Therefore, the GCF of Fractions 366/31,278/63,666/63 is 2/1953
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 31,63,63 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,63,63) = 1
common factors(in case of two or more numbers have common factors) = 63
GCF(31,63,63) x common factors =1 x 63 = 63
LCM(31,63,63) = ( 31 × 63 × 63 ) / 63
LCM(31,63,63) = 123039 / 63
LCM(31,63,63) = 1953
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 366,278,666?
The HCF of 366,278,666 is 2
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 366/31, 278/63, 666/63?
Answer: GCF of Numerators as per given numbers 366/31, 278/63, 666/63 is
GCF of Numerators i.e. for 366,278,666 is 2
LCM of denominators i.e. for 31,63,63 is 1953.
Thus, GCF of Fractions is 2/1953.Finally, GCF of Fractions for 366/31, 278/63, 666/63 is 2/1953.