Use our free GCF of Fractions Calculator tool to compute the GCF of 69/64, 28/85, 96/81, 21/92 i.e 1/10134720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 69/64, 28/85, 96/81, 21/92.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 69/64,28/85,96/81,21/92
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 69/64,28/85,96/81,21/92, numerators are 69,28,96,21
Denominators are 64,85,81,92
The GCF of 69,28,96,21 is 1 .
LCM of 64,85,81,92 is 10134720.
The greatest common factor of 69/64,28/85,96/81,21/92 = [GCF of 69,28,96,21]/[LCM of 64,85,81,92]= 1/10134720
Therefore, the GCF of 69/64,28/85,96/81,21/92 is 1/10134720.
To find the highest common factor of 69,28,96,21, we have to find the factors of both numbers and list the highest common factor.
The factors of 69 are 1, 3, 23, 69
The factors of 28 are 1, 2, 4, 7, 14, 28
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 21 are 1, 3, 7, 21
The HCF of 69,28,96,21 is 1.
Lets's calculate GCF of 69,28,96,21
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 69
:1,3,23,69
Now, list down the factors of 28
:1,2,4,7,14,28
Now, list down the factors of 96
:1,2,3,4,6,8,12,16,24,32,48,96
Now, list down the factors of 21
:1,3,7,21
Greatest Common Factor
We found the factors 69,28,96,21 . The biggest common factor number is the GCF number.
So the greatest common factor 69,28,96,21 is 1.
Lets's calculate LCM of 64,85,81,92
2 | 64, 85, 81, 92 |
2 | 32, 85, 81, 46 |
16, 85, 81, 23 |
∴ So the LCM of the given numbers is 2 x 2 x 16 x 85 x 81 x 23 = 10134720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10134720
Therefore, the GCF of Fractions 69/64,28/85,96/81,21/92 is 1/10134720
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 64,85,81,92 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(64,85,81,92) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(64,85,81,92) x common factors =1 x 4 = 4
LCM(64,85,81,92) = ( 64 × 85 × 81 × 92 ) / 4
LCM(64,85,81,92) = 40538880 / 4
LCM(64,85,81,92) = 10134720
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 69,28,96,21?
The HCF of 69,28,96,21 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 69/64, 28/85, 96/81, 21/92?
Answer: GCF of Numerators as per given numbers 69/64, 28/85, 96/81, 21/92 is
GCF of Numerators i.e. for 69,28,96,21 is 1
LCM of denominators i.e. for 64,85,81,92 is 10134720.
Thus, GCF of Fractions is 1/10134720.Finally, GCF of Fractions for 69/64, 28/85, 96/81, 21/92 is 1/10134720.