Use our free GCF of Fractions Calculator tool to compute the GCF of 165/749, 145/107 i.e 5/749 easily. The following is the detailed procedure to determine the greatest common factor of fractions 165/749, 145/107.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 165/749,145/107
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 165/749,145/107, numerators are 165,145
Denominators are 749,107
The GCF of 165,145 is 5 .
LCM of 749,107 is 749.
The greatest common factor of 165/749,145/107 = [GCF of 165,145]/[LCM of 749,107]= 5/749
Therefore, the GCF of 165/749,145/107 is 5/749.
To find the highest common factor of 165,145, we have to find the factors of both numbers and list the highest common factor.
The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165
The factors of 145 are 1, 5, 29, 145
The HCF of 165,145 is 5.
Lets's calculate GCF of 165,145
5 | 165, 145 |
33, 29 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 165
:1,3,5,11,15,33,55,165
Now, list down the factors of 145
:1,5,29,145
Greatest Common Factor
We found the factors 165,145 . The biggest common factor number is the GCF number.
So the greatest common factor 165,145 is 5.
Lets's calculate LCM of 749,107
107 | 749, 107 |
7, 1 |
∴ So the LCM of the given numbers is 107 x 7 x 1 = 749
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/749
Therefore, the GCF of Fractions 165/749,145/107 is 5/749
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 749,107 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(749,107) = 107
common factors(in case of two or more numbers have common factors) = 1
GCF(749,107) x common factors =107 x 1 = 107
LCM(749,107) = ( 749 × 107 ) / 107
LCM(749,107) = 80143 / 107
LCM(749,107) = 749
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 165,145?
The HCF of 165,145 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 165/749, 145/107?
Answer: GCF of Numerators as per given numbers 165/749, 145/107 is
GCF of Numerators i.e. for 165,145 is 5
LCM of denominators i.e. for 749,107 is 749.
Thus, GCF of Fractions is 5/749.Finally, GCF of Fractions for 165/749, 145/107 is 5/749.