Use our free GCF of Fractions Calculator tool to compute the GCF of 72/120, 468/778, 360/644 i.e 36/7515480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 72/120, 468/778, 360/644.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 72/120,468/778,360/644
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 72/120,468/778,360/644, numerators are 72,468,360
Denominators are 120,778,644
The GCF of 72,468,360 is 36 .
LCM of 120,778,644 is 7515480.
The greatest common factor of 72/120,468/778,360/644 = [GCF of 72,468,360]/[LCM of 120,778,644]= 36/7515480
Therefore, the GCF of 72/120,468/778,360/644 is 36/7515480.
To find the highest common factor of 72,468,360, we have to find the factors of both numbers and list the highest common factor.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468
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 HCF of 72,468,360 is 36.
Lets's calculate GCF of 72,468,360
2 | 72, 468, 360 |
2 | 36, 234, 180 |
3 | 18, 117, 90 |
3 | 6, 39, 30 |
2, 13, 10 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Now, list down the factors of 468
:1,2,3,4,6,9,12,13,18,26,36,39,52,78,117,156,234,468
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
Greatest Common Factor
We found the factors 72,468,360 . The biggest common factor number is the GCF number.
So the greatest common factor 72,468,360 is 36.
Lets's calculate LCM of 120,778,644
2 | 120, 778, 644 |
2 | 60, 389, 322 |
30, 389, 161 |
∴ So the LCM of the given numbers is 2 x 2 x 30 x 389 x 161 = 7515480
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/7515480
Therefore, the GCF of Fractions 72/120,468/778,360/644 is 36/7515480
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 120,778,644 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(120,778,644) = 2
common factors(in case of two or more numbers have common factors) = 4
GCF(120,778,644) x common factors =2 x 4 = 8
LCM(120,778,644) = ( 120 × 778 × 644 ) / 8
LCM(120,778,644) = 60123840 / 8
LCM(120,778,644) = 7515480
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 72,468,360?
The HCF of 72,468,360 is 36
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 72/120, 468/778, 360/644?
Answer: GCF of Numerators as per given numbers 72/120, 468/778, 360/644 is
GCF of Numerators i.e. for 72,468,360 is 36
LCM of denominators i.e. for 120,778,644 is 7515480.
Thus, GCF of Fractions is 36/7515480.Finally, GCF of Fractions for 72/120, 468/778, 360/644 is 36/7515480.