Use our free GCF of Fractions Calculator tool to compute the GCF of 360/725, 160/768 i.e 40/556800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 360/725, 160/768.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 360/725,160/768
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 360/725,160/768, numerators are 360,160
Denominators are 725,768
The GCF of 360,160 is 40 .
LCM of 725,768 is 556800.
The greatest common factor of 360/725,160/768 = [GCF of 360,160]/[LCM of 725,768]= 40/556800
Therefore, the GCF of 360/725,160/768 is 40/556800.
To find the highest common factor of 360,160, we have to find the factors of both numbers and list the highest common factor.
The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
The HCF of 360,160 is 40.
Lets's calculate GCF of 360,160
2 | 360, 160 |
2 | 180, 80 |
2 | 90, 40 |
5 | 45, 20 |
9, 4 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40
Now, list down the factors of 360
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360
Now, list down the factors of 160
:1,2,4,5,8,10,16,20,32,40,80,160
Greatest Common Factor
We found the factors 360,160 . The biggest common factor number is the GCF number.
So the greatest common factor 360,160 is 40.
Lets's calculate LCM of 725,768
Given numbers has no common factors except 1. So, there LCM is their product i.e 556800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/556800
Therefore, the GCF of Fractions 360/725,160/768 is 40/556800
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 725,768 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(725,768) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(725,768) x common factors =1 x 1 = 1
LCM(725,768) = ( 725 × 768 ) / 1
LCM(725,768) = 556800 / 1
LCM(725,768) = 556800
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 360,160?
The HCF of 360,160 is 40
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 360/725, 160/768?
Answer: GCF of Numerators as per given numbers 360/725, 160/768 is
GCF of Numerators i.e. for 360,160 is 40
LCM of denominators i.e. for 725,768 is 556800.
Thus, GCF of Fractions is 40/556800.Finally, GCF of Fractions for 360/725, 160/768 is 40/556800.