Use our free GCF of Fractions Calculator tool to compute the GCF of 370/408, 150/229 i.e 10/93432 easily. The following is the detailed procedure to determine the greatest common factor of fractions 370/408, 150/229.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 370/408,150/229
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 370/408,150/229, numerators are 370,150
Denominators are 408,229
The GCF of 370,150 is 10 .
LCM of 408,229 is 93432.
The greatest common factor of 370/408,150/229 = [GCF of 370,150]/[LCM of 408,229]= 10/93432
Therefore, the GCF of 370/408,150/229 is 10/93432.
To find the highest common factor of 370,150, we have to find the factors of both numbers and list the highest common factor.
The factors of 370 are 1, 2, 5, 10, 37, 74, 185, 370
The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
The HCF of 370,150 is 10.
Lets's calculate GCF of 370,150
2 | 370, 150 |
5 | 185, 75 |
37, 15 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Now, list down the factors of 370
:1,2,5,10,37,74,185,370
Now, list down the factors of 150
:1,2,3,5,6,10,15,25,30,50,75,150
Greatest Common Factor
We found the factors 370,150 . The biggest common factor number is the GCF number.
So the greatest common factor 370,150 is 10.
Lets's calculate LCM of 408,229
Given numbers has no common factors except 1. So, there LCM is their product i.e 93432
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/93432
Therefore, the GCF of Fractions 370/408,150/229 is 10/93432
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 408,229 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(408,229) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(408,229) x common factors =1 x 1 = 1
LCM(408,229) = ( 408 × 229 ) / 1
LCM(408,229) = 93432 / 1
LCM(408,229) = 93432
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 370,150?
The HCF of 370,150 is 10
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 370/408, 150/229?
Answer: GCF of Numerators as per given numbers 370/408, 150/229 is
GCF of Numerators i.e. for 370,150 is 10
LCM of denominators i.e. for 408,229 is 93432.
Thus, GCF of Fractions is 10/93432.Finally, GCF of Fractions for 370/408, 150/229 is 10/93432.