Use our free GCF of Fractions Calculator tool to compute the GCF of 450/961, 510/634 i.e 30/609274 easily. The following is the detailed procedure to determine the greatest common factor of fractions 450/961, 510/634.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 450/961,510/634
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 450/961,510/634, numerators are 450,510
Denominators are 961,634
The GCF of 450,510 is 30 .
LCM of 961,634 is 609274.
The greatest common factor of 450/961,510/634 = [GCF of 450,510]/[LCM of 961,634]= 30/609274
Therefore, the GCF of 450/961,510/634 is 30/609274.
To find the highest common factor of 450,510, we have to find the factors of both numbers and list the highest common factor.
The factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
The HCF of 450,510 is 30.
Lets's calculate GCF of 450,510
2 | 450, 510 |
3 | 225, 255 |
5 | 75, 85 |
15, 17 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Now, list down the factors of 450
:1,2,3,5,6,9,10,15,18,25,30,45,50,75,90,150,225,450
Now, list down the factors of 510
:1,2,3,5,6,10,15,17,30,34,51,85,102,170,255,510
Greatest Common Factor
We found the factors 450,510 . The biggest common factor number is the GCF number.
So the greatest common factor 450,510 is 30.
Lets's calculate LCM of 961,634
Given numbers has no common factors except 1. So, there LCM is their product i.e 609274
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/609274
Therefore, the GCF of Fractions 450/961,510/634 is 30/609274
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 961,634 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(961,634) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(961,634) x common factors =1 x 1 = 1
LCM(961,634) = ( 961 × 634 ) / 1
LCM(961,634) = 609274 / 1
LCM(961,634) = 609274
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 450,510?
The HCF of 450,510 is 30
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 450/961, 510/634?
Answer: GCF of Numerators as per given numbers 450/961, 510/634 is
GCF of Numerators i.e. for 450,510 is 30
LCM of denominators i.e. for 961,634 is 609274.
Thus, GCF of Fractions is 30/609274.Finally, GCF of Fractions for 450/961, 510/634 is 30/609274.