Use our free GCF of Fractions Calculator tool to compute the GCF of 720/767, 678/532 i.e 6/408044 easily. The following is the detailed procedure to determine the greatest common factor of fractions 720/767, 678/532.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 720/767,678/532
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 720/767,678/532, numerators are 720,678
Denominators are 767,532
The GCF of 720,678 is 6 .
LCM of 767,532 is 408044.
The greatest common factor of 720/767,678/532 = [GCF of 720,678]/[LCM of 767,532]= 6/408044
Therefore, the GCF of 720/767,678/532 is 6/408044.
To find the highest common factor of 720,678, we have to find the factors of both numbers and list the highest common factor.
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 factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The HCF of 720,678 is 6.
Lets's calculate GCF of 720,678
2 | 720, 678 |
3 | 360, 339 |
120, 113 |
∴ So the GCF of the given numbers is 2 x 3 = 6
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
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Greatest Common Factor
We found the factors 720,678 . The biggest common factor number is the GCF number.
So the greatest common factor 720,678 is 6.
Lets's calculate LCM of 767,532
Given numbers has no common factors except 1. So, there LCM is their product i.e 408044
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/408044
Therefore, the GCF of Fractions 720/767,678/532 is 6/408044
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 767,532 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(767,532) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(767,532) x common factors =1 x 1 = 1
LCM(767,532) = ( 767 × 532 ) / 1
LCM(767,532) = 408044 / 1
LCM(767,532) = 408044
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 720,678?
The HCF of 720,678 is 6
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 720/767, 678/532?
Answer: GCF of Numerators as per given numbers 720/767, 678/532 is
GCF of Numerators i.e. for 720,678 is 6
LCM of denominators i.e. for 767,532 is 408044.
Thus, GCF of Fractions is 6/408044.Finally, GCF of Fractions for 720/767, 678/532 is 6/408044.