Use our free GCF of Fractions Calculator tool to compute the GCF of 16/65, 64/85, 51/40, 90/21 i.e 1/185640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 16/65, 64/85, 51/40, 90/21.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 16/65,64/85,51/40,90/21
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 16/65,64/85,51/40,90/21, numerators are 16,64,51,90
Denominators are 65,85,40,21
The GCF of 16,64,51,90 is 1 .
LCM of 65,85,40,21 is 185640.
The greatest common factor of 16/65,64/85,51/40,90/21 = [GCF of 16,64,51,90]/[LCM of 65,85,40,21]= 1/185640
Therefore, the GCF of 16/65,64/85,51/40,90/21 is 1/185640.
To find the highest common factor of 16,64,51,90, we have to find the factors of both numbers and list the highest common factor.
The factors of 16 are 1, 2, 4, 8, 16
The factors of 64 are 1, 2, 4, 8, 16, 32, 64
The factors of 51 are 1, 3, 17, 51
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The HCF of 16,64,51,90 is 1.
Lets's calculate GCF of 16,64,51,90
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 16
:1,2,4,8,16
Now, list down the factors of 64
:1,2,4,8,16,32,64
Now, list down the factors of 51
:1,3,17,51
Now, list down the factors of 90
:1,2,3,5,6,9,10,15,18,30,45,90
Greatest Common Factor
We found the factors 16,64,51,90 . The biggest common factor number is the GCF number.
So the greatest common factor 16,64,51,90 is 1.
Lets's calculate LCM of 65,85,40,21
5 | 65, 85, 40, 21 |
13, 17, 8, 21 |
∴ So the LCM of the given numbers is 5 x 13 x 17 x 8 x 21 = 185640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/185640
Therefore, the GCF of Fractions 16/65,64/85,51/40,90/21 is 1/185640
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 65,85,40,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,85,40,21) = 1
common factors(in case of two or more numbers have common factors) = 25
GCF(65,85,40,21) x common factors =1 x 25 = 25
LCM(65,85,40,21) = ( 65 × 85 × 40 × 21 ) / 25
LCM(65,85,40,21) = 4641000 / 25
LCM(65,85,40,21) = 185640
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 16,64,51,90?
The HCF of 16,64,51,90 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 16/65, 64/85, 51/40, 90/21?
Answer: GCF of Numerators as per given numbers 16/65, 64/85, 51/40, 90/21 is
GCF of Numerators i.e. for 16,64,51,90 is 1
LCM of denominators i.e. for 65,85,40,21 is 185640.
Thus, GCF of Fractions is 1/185640.Finally, GCF of Fractions for 16/65, 64/85, 51/40, 90/21 is 1/185640.