Use our free GCF of Fractions Calculator tool to compute the GCF of 28/51, 66/38, 45/29, 89/17 i.e 1/56202 easily. The following is the detailed procedure to determine the greatest common factor of fractions 28/51, 66/38, 45/29, 89/17.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 28/51,66/38,45/29,89/17
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 28/51,66/38,45/29,89/17, numerators are 28,66,45,89
Denominators are 51,38,29,17
The GCF of 28,66,45,89 is 1 .
LCM of 51,38,29,17 is 56202.
The greatest common factor of 28/51,66/38,45/29,89/17 = [GCF of 28,66,45,89]/[LCM of 51,38,29,17]= 1/56202
Therefore, the GCF of 28/51,66/38,45/29,89/17 is 1/56202.
To find the highest common factor of 28,66,45,89, we have to find the factors of both numbers and list the highest common factor.
The factors of 28 are 1, 2, 4, 7, 14, 28
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66
The factors of 45 are 1, 3, 5, 9, 15, 45
The factors of 89 are 1, 89
The HCF of 28,66,45,89 is 1.
Lets's calculate GCF of 28,66,45,89
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 28
:1,2,4,7,14,28
Now, list down the factors of 66
:1,2,3,6,11,22,33,66
Now, list down the factors of 45
:1,3,5,9,15,45
Now, list down the factors of 89
:1,89
Greatest Common Factor
We found the factors 28,66,45,89 . The biggest common factor number is the GCF number.
So the greatest common factor 28,66,45,89 is 1.
Lets's calculate LCM of 51,38,29,17
17 | 51, 38, 29, 17 |
3, 38, 29, 1 |
∴ So the LCM of the given numbers is 17 x 3 x 38 x 29 x 1 = 56202
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/56202
Therefore, the GCF of Fractions 28/51,66/38,45/29,89/17 is 1/56202
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 51,38,29,17 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,38,29,17) = 1
common factors(in case of two or more numbers have common factors) = 17
GCF(51,38,29,17) x common factors =1 x 17 = 17
LCM(51,38,29,17) = ( 51 × 38 × 29 × 17 ) / 17
LCM(51,38,29,17) = 955434 / 17
LCM(51,38,29,17) = 56202
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 28,66,45,89?
The HCF of 28,66,45,89 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 28/51, 66/38, 45/29, 89/17?
Answer: GCF of Numerators as per given numbers 28/51, 66/38, 45/29, 89/17 is
GCF of Numerators i.e. for 28,66,45,89 is 1
LCM of denominators i.e. for 51,38,29,17 is 56202.
Thus, GCF of Fractions is 1/56202.Finally, GCF of Fractions for 28/51, 66/38, 45/29, 89/17 is 1/56202.