Use our free GCF of Fractions Calculator tool to compute the GCF of 21/120, 79/7680 i.e 1/7680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/120, 79/7680.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 21/120,79/7680
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 21/120,79/7680, numerators are 21,79
Denominators are 120,7680
The GCF of 21,79 is 1 .
LCM of 120,7680 is 7680.
The greatest common factor of 21/120,79/7680 = [GCF of 21,79]/[LCM of 120,7680]= 1/7680
Therefore, the GCF of 21/120,79/7680 is 1/7680.
To find the highest common factor of 21,79, 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 79 are 1, 79
The HCF of 21,79 is 1.
Lets's calculate GCF of 21,79
∴ So GCF of numbers is 1 because of no common factors present between them.
Lets's calculate LCM of 120,7680
2 | 120, 7680 |
2 | 60, 3840 |
2 | 30, 1920 |
3 | 15, 960 |
5 | 5, 320 |
1, 64 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 1 x 64 = 7680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7680
Therefore, the GCF of Fractions 21/120,79/7680 is 1/7680
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 120,7680 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(120,7680) = 120
common factors(in case of two or more numbers have common factors) = 1
GCF(120,7680) x common factors =120 x 1 = 120
LCM(120,7680) = ( 120 × 7680 ) / 120
LCM(120,7680) = 921600 / 120
LCM(120,7680) = 7680
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 21,79?
The HCF of 21,79 is 1
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 21/120, 79/7680?
Answer: GCF of Numerators as per given numbers 21/120, 79/7680 is
GCF of Numerators i.e. for 21,79 is 1
LCM of denominators i.e. for 120,7680 is 7680.
Thus, GCF of Fractions is 1/7680.Finally, GCF of Fractions for 21/120, 79/7680 is 1/7680.