Use our free GCF of Fractions Calculator tool to compute the GCF of 23/99, 208/18, 169/682 i.e 1/6138 easily. The following is the detailed procedure to determine the greatest common factor of fractions 23/99, 208/18, 169/682.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 23/99,208/18,169/682
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 23/99,208/18,169/682, numerators are 23,208,169
Denominators are 99,18,682
The GCF of 23,208,169 is 1 .
LCM of 99,18,682 is 6138.
The greatest common factor of 23/99,208/18,169/682 = [GCF of 23,208,169]/[LCM of 99,18,682]= 1/6138
Therefore, the GCF of 23/99,208/18,169/682 is 1/6138.
To find the highest common factor of 23,208,169, we have to find the factors of both numbers and list the highest common factor.
The factors of 23 are 1, 23
The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
The factors of 169 are 1, 13, 169
The HCF of 23,208,169 is 1.
Lets's calculate GCF of 23,208,169
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 23
:1,23
Now, list down the factors of 208
:1,2,4,8,13,16,26,52,104,208
Now, list down the factors of 169
:1,13,169
Greatest Common Factor
We found the factors 23,208,169 . The biggest common factor number is the GCF number.
So the greatest common factor 23,208,169 is 1.
Lets's calculate LCM of 99,18,682
2 | 99, 18, 682 |
3 | 99, 9, 341 |
3 | 33, 3, 341 |
11 | 11, 1, 341 |
1, 1, 31 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 11 x 1 x 1 x 31 = 6138
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6138
Therefore, the GCF of Fractions 23/99,208/18,169/682 is 1/6138
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 99,18,682 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(99,18,682) = 1
common factors(in case of two or more numbers have common factors) = 198
GCF(99,18,682) x common factors =1 x 198 = 198
LCM(99,18,682) = ( 99 × 18 × 682 ) / 198
LCM(99,18,682) = 1215324 / 198
LCM(99,18,682) = 6138
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 23,208,169?
The HCF of 23,208,169 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 23/99, 208/18, 169/682?
Answer: GCF of Numerators as per given numbers 23/99, 208/18, 169/682 is
GCF of Numerators i.e. for 23,208,169 is 1
LCM of denominators i.e. for 99,18,682 is 6138.
Thus, GCF of Fractions is 1/6138.Finally, GCF of Fractions for 23/99, 208/18, 169/682 is 1/6138.