Use our free GCF of Fractions Calculator tool to compute the GCF of 310/640, 720/907 i.e 10/580480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 310/640, 720/907.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 310/640,720/907
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 310/640,720/907, numerators are 310,720
Denominators are 640,907
The GCF of 310,720 is 10 .
LCM of 640,907 is 580480.
The greatest common factor of 310/640,720/907 = [GCF of 310,720]/[LCM of 640,907]= 10/580480
Therefore, the GCF of 310/640,720/907 is 10/580480.
To find the highest common factor of 310,720, we have to find the factors of both numbers and list the highest common factor.
The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310
The factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720
The HCF of 310,720 is 10.
Lets's calculate GCF of 310,720
2 | 310, 720 |
5 | 155, 360 |
31, 72 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Now, list down the factors of 310
:1,2,5,10,31,62,155,310
Now, list down the factors of 720
:1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,36,40,45,48,60,72,80,90,120,144,180,240,360,720
Greatest Common Factor
We found the factors 310,720 . The biggest common factor number is the GCF number.
So the greatest common factor 310,720 is 10.
Lets's calculate LCM of 640,907
Given numbers has no common factors except 1. So, there LCM is their product i.e 580480
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/580480
Therefore, the GCF of Fractions 310/640,720/907 is 10/580480
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 640,907 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(640,907) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(640,907) x common factors =1 x 1 = 1
LCM(640,907) = ( 640 × 907 ) / 1
LCM(640,907) = 580480 / 1
LCM(640,907) = 580480
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 310,720?
The HCF of 310,720 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 310/640, 720/907?
Answer: GCF of Numerators as per given numbers 310/640, 720/907 is
GCF of Numerators i.e. for 310,720 is 10
LCM of denominators i.e. for 640,907 is 580480.
Thus, GCF of Fractions is 10/580480.Finally, GCF of Fractions for 310/640, 720/907 is 10/580480.