Use our free GCF of Fractions Calculator tool to compute the GCF of 660/708, 465/975 i.e 15/230100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 660/708, 465/975.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 660/708,465/975
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 660/708,465/975, numerators are 660,465
Denominators are 708,975
The GCF of 660,465 is 15 .
LCM of 708,975 is 230100.
The greatest common factor of 660/708,465/975 = [GCF of 660,465]/[LCM of 708,975]= 15/230100
Therefore, the GCF of 660/708,465/975 is 15/230100.
To find the highest common factor of 660,465, we have to find the factors of both numbers and list the highest common factor.
The factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660
The factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465
The HCF of 660,465 is 15.
Lets's calculate GCF of 660,465
3 | 660, 465 |
5 | 220, 155 |
44, 31 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Now, list down the factors of 660
:1,2,3,4,5,6,10,11,12,15,20,22,30,33,44,55,60,66,110,132,165,220,330,660
Now, list down the factors of 465
:1,3,5,15,31,93,155,465
Greatest Common Factor
We found the factors 660,465 . The biggest common factor number is the GCF number.
So the greatest common factor 660,465 is 15.
Lets's calculate LCM of 708,975
3 | 708, 975 |
236, 325 |
∴ So the LCM of the given numbers is 3 x 236 x 325 = 230100
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/230100
Therefore, the GCF of Fractions 660/708,465/975 is 15/230100
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 708,975 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(708,975) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(708,975) x common factors =3 x 1 = 3
LCM(708,975) = ( 708 × 975 ) / 3
LCM(708,975) = 690300 / 3
LCM(708,975) = 230100
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 660,465?
The HCF of 660,465 is 15
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 660/708, 465/975?
Answer: GCF of Numerators as per given numbers 660/708, 465/975 is
GCF of Numerators i.e. for 660,465 is 15
LCM of denominators i.e. for 708,975 is 230100.
Thus, GCF of Fractions is 15/230100.Finally, GCF of Fractions for 660/708, 465/975 is 15/230100.