Use our free GCF of Fractions Calculator tool to compute the GCF of 21/360, 54/7440 i.e 3/22320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/360, 54/7440.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 21/360,54/7440
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 21/360,54/7440, numerators are 21,54
Denominators are 360,7440
The GCF of 21,54 is 3 .
LCM of 360,7440 is 22320.
The greatest common factor of 21/360,54/7440 = [GCF of 21,54]/[LCM of 360,7440]= 3/22320
Therefore, the GCF of 21/360,54/7440 is 3/22320.
To find the highest common factor of 21,54, we have to find the factors of both numbers and list the highest common factor.
The factors of 21 are 1, 3, 7, 21
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
The HCF of 21,54 is 3.
Lets's calculate GCF of 21,54
3 | 21, 54 |
7, 18 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 54
:1,2,3,6,9,18,27,54
Greatest Common Factor
We found the factors 21,54 . The biggest common factor number is the GCF number.
So the greatest common factor 21,54 is 3.
Lets's calculate LCM of 360,7440
2 | 360, 7440 |
2 | 180, 3720 |
2 | 90, 1860 |
3 | 45, 930 |
5 | 15, 310 |
3, 62 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 3 x 62 = 22320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/22320
Therefore, the GCF of Fractions 21/360,54/7440 is 3/22320
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 360,7440 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(360,7440) = 120
common factors(in case of two or more numbers have common factors) = 1
GCF(360,7440) x common factors =120 x 1 = 120
LCM(360,7440) = ( 360 × 7440 ) / 120
LCM(360,7440) = 2678400 / 120
LCM(360,7440) = 22320
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 21,54?
The HCF of 21,54 is 3
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 21/360, 54/7440?
Answer: GCF of Numerators as per given numbers 21/360, 54/7440 is
GCF of Numerators i.e. for 21,54 is 3
LCM of denominators i.e. for 360,7440 is 22320.
Thus, GCF of Fractions is 3/22320.Finally, GCF of Fractions for 21/360, 54/7440 is 3/22320.