Use our free GCF of Fractions Calculator tool to compute the GCF of 432/130, 400/579 i.e 16/75270 easily. The following is the detailed procedure to determine the greatest common factor of fractions 432/130, 400/579.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 432/130,400/579
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 432/130,400/579, numerators are 432,400
Denominators are 130,579
The GCF of 432,400 is 16 .
LCM of 130,579 is 75270.
The greatest common factor of 432/130,400/579 = [GCF of 432,400]/[LCM of 130,579]= 16/75270
Therefore, the GCF of 432/130,400/579 is 16/75270.
To find the highest common factor of 432,400, we have to find the factors of both numbers and list the highest common factor.
The factors of 432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432
The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
The HCF of 432,400 is 16.
Lets's calculate GCF of 432,400
2 | 432, 400 |
2 | 216, 200 |
2 | 108, 100 |
2 | 54, 50 |
27, 25 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Now, list down the factors of 432
:1,2,3,4,6,8,9,12,16,18,24,27,36,48,54,72,108,144,216,432
Now, list down the factors of 400
:1,2,4,5,8,10,16,20,25,40,50,80,100,200,400
Greatest Common Factor
We found the factors 432,400 . The biggest common factor number is the GCF number.
So the greatest common factor 432,400 is 16.
Lets's calculate LCM of 130,579
Given numbers has no common factors except 1. So, there LCM is their product i.e 75270
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/75270
Therefore, the GCF of Fractions 432/130,400/579 is 16/75270
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 130,579 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(130,579) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(130,579) x common factors =1 x 1 = 1
LCM(130,579) = ( 130 × 579 ) / 1
LCM(130,579) = 75270 / 1
LCM(130,579) = 75270
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 432,400?
The HCF of 432,400 is 16
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 432/130, 400/579?
Answer: GCF of Numerators as per given numbers 432/130, 400/579 is
GCF of Numerators i.e. for 432,400 is 16
LCM of denominators i.e. for 130,579 is 75270.
Thus, GCF of Fractions is 16/75270.Finally, GCF of Fractions for 432/130, 400/579 is 16/75270.