Use our free GCF of Fractions Calculator tool to compute the GCF of 855/456, 714/153 i.e 3/23256 easily. The following is the detailed procedure to determine the greatest common factor of fractions 855/456, 714/153.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 855/456,714/153
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 855/456,714/153, numerators are 855,714
Denominators are 456,153
The GCF of 855,714 is 3 .
LCM of 456,153 is 23256.
The greatest common factor of 855/456,714/153 = [GCF of 855,714]/[LCM of 456,153]= 3/23256
Therefore, the GCF of 855/456,714/153 is 3/23256.
To find the highest common factor of 855,714, we have to find the factors of both numbers and list the highest common factor.
The factors of 855 are 1, 3, 5, 9, 15, 19, 45, 57, 95, 171, 285, 855
The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
The HCF of 855,714 is 3.
Lets's calculate GCF of 855,714
3 | 855, 714 |
285, 238 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 855
:1,3,5,9,15,19,45,57,95,171,285,855
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 855,714 . The biggest common factor number is the GCF number.
So the greatest common factor 855,714 is 3.
Lets's calculate LCM of 456,153
3 | 456, 153 |
152, 51 |
∴ So the LCM of the given numbers is 3 x 152 x 51 = 23256
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/23256
Therefore, the GCF of Fractions 855/456,714/153 is 3/23256
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 456,153 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(456,153) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(456,153) x common factors =3 x 1 = 3
LCM(456,153) = ( 456 × 153 ) / 3
LCM(456,153) = 69768 / 3
LCM(456,153) = 23256
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 855,714?
The HCF of 855,714 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 855/456, 714/153?
Answer: GCF of Numerators as per given numbers 855/456, 714/153 is
GCF of Numerators i.e. for 855,714 is 3
LCM of denominators i.e. for 456,153 is 23256.
Thus, GCF of Fractions is 3/23256.Finally, GCF of Fractions for 855/456, 714/153 is 3/23256.