Use our free GCF of Fractions Calculator tool to compute the GCF of 7565/748, 1700/347 i.e 85/259556 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7565/748, 1700/347.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 7565/748,1700/347
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 7565/748,1700/347, numerators are 7565,1700
Denominators are 748,347
The GCF of 7565,1700 is 85 .
LCM of 748,347 is 259556.
The greatest common factor of 7565/748,1700/347 = [GCF of 7565,1700]/[LCM of 748,347]= 85/259556
Therefore, the GCF of 7565/748,1700/347 is 85/259556.
To find the highest common factor of 7565,1700, we have to find the factors of both numbers and list the highest common factor.
The factors of 7565 are 1, 5, 17, 85, 89, 445, 1513, 7565
The factors of 1700 are 1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, 850, 1700
The HCF of 7565,1700 is 85.
Lets's calculate GCF of 7565,1700
5 | 7565, 1700 |
17 | 1513, 340 |
89, 20 |
∴ So the GCF of the given numbers is 5 x 17 = 85
Now, list down the factors of 7565
:1,5,17,85,89,445,1513,7565
Now, list down the factors of 1700
:1,2,4,5,10,17,20,25,34,50,68,85,100,170,340,425,850,1700
Greatest Common Factor
We found the factors 7565,1700 . The biggest common factor number is the GCF number.
So the greatest common factor 7565,1700 is 85.
Lets's calculate LCM of 748,347
Given numbers has no common factors except 1. So, there LCM is their product i.e 259556
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 85/259556
Therefore, the GCF of Fractions 7565/748,1700/347 is 85/259556
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 748,347 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(748,347) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(748,347) x common factors =1 x 1 = 1
LCM(748,347) = ( 748 × 347 ) / 1
LCM(748,347) = 259556 / 1
LCM(748,347) = 259556
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 7565,1700?
The HCF of 7565,1700 is 85
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 7565/748, 1700/347?
Answer: GCF of Numerators as per given numbers 7565/748, 1700/347 is
GCF of Numerators i.e. for 7565,1700 is 85
LCM of denominators i.e. for 748,347 is 259556.
Thus, GCF of Fractions is 85/259556.Finally, GCF of Fractions for 7565/748, 1700/347 is 85/259556.