Use our free GCF of Fractions Calculator tool to compute the GCF of 100/289, 745/462 i.e 5/133518 easily. The following is the detailed procedure to determine the greatest common factor of fractions 100/289, 745/462.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 100/289,745/462
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 100/289,745/462, numerators are 100,745
Denominators are 289,462
The GCF of 100,745 is 5 .
LCM of 289,462 is 133518.
The greatest common factor of 100/289,745/462 = [GCF of 100,745]/[LCM of 289,462]= 5/133518
Therefore, the GCF of 100/289,745/462 is 5/133518.
To find the highest common factor of 100,745, we have to find the factors of both numbers and list the highest common factor.
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100
The factors of 745 are 1, 5, 149, 745
The HCF of 100,745 is 5.
Lets's calculate GCF of 100,745
5 | 100, 745 |
20, 149 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 100
:1,2,4,5,10,20,25,50,100
Now, list down the factors of 745
:1,5,149,745
Greatest Common Factor
We found the factors 100,745 . The biggest common factor number is the GCF number.
So the greatest common factor 100,745 is 5.
Lets's calculate LCM of 289,462
Given numbers has no common factors except 1. So, there LCM is their product i.e 133518
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/133518
Therefore, the GCF of Fractions 100/289,745/462 is 5/133518
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 289,462 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(289,462) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(289,462) x common factors =1 x 1 = 1
LCM(289,462) = ( 289 × 462 ) / 1
LCM(289,462) = 133518 / 1
LCM(289,462) = 133518
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 100,745?
The HCF of 100,745 is 5
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 100/289, 745/462?
Answer: GCF of Numerators as per given numbers 100/289, 745/462 is
GCF of Numerators i.e. for 100,745 is 5
LCM of denominators i.e. for 289,462 is 133518.
Thus, GCF of Fractions is 5/133518.Finally, GCF of Fractions for 100/289, 745/462 is 5/133518.