GCF of 1575/720, 1209/754
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1575/720, 1209/754 i.e 3/271440 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1575/720, 1209/754.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 1575/720,1209/754?
Given fractions are 1575/720,1209/754
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 1575/720,1209/754, numerators are 1575,1209
Denominators are 720,754
The GCF of 1575,1209 is 3 .
LCM of 720,754 is 271440.
The greatest common factor of 1575/720,1209/754 = [GCF of 1575,1209]/[LCM of 720,754]= 3/271440
Therefore, the GCF of 1575/720,1209/754 is 3/271440.
To find the highest common factor of 1575,1209, we have to find the factors of both numbers and list the highest common factor.
The factors of 1575 are 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525, 1575
The factors of 1209 are 1, 3, 13, 31, 39, 93, 403, 1209
The HCF of 1575,1209 is 3.
Lets's calculate GCF of 1575,1209
| 3 | 1575, 1209 |
| 525, 403 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 1575,1209 By Matching Biggest Common Factor Method
Now, list down the factors of 1575
:1,3,5,7,9,15,21,25,35,45,63,75,105,175,225,315,525,1575
Now, list down the factors of 1209
:1,3,13,31,39,93,403,1209
Greatest Common Factor
We found the factors 1575,1209 . The biggest common factor number is the GCF number.
So the greatest common factor 1575,1209 is 3.
Lets's calculate LCM of 720,754
| 2 | 720, 754 |
| 360, 377 |
∴ So the LCM of the given numbers is 2 x 360 x 377 = 271440
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/271440
Therefore, the GCF of Fractions 1575/720,1209/754 is 3/271440
Least Common Multiple of 720,754 with GCF Formula
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 720,754 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(720,754) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(720,754) x common factors =2 x 1 = 2
LCM(720,754) = ( 720 × 754 ) / 2
LCM(720,754) = 542880 / 2
LCM(720,754) = 271440
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 1575/720, 1209/754
1. What is the HCF of 1575,1209?
The HCF of 1575,1209 is 3
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 1575/720, 1209/754?
Answer: GCF of Numerators as per given numbers 1575/720, 1209/754 is
GCF of Numerators i.e. for 1575,1209 is 3
LCM of denominators i.e. for 720,754 is 271440.
Thus, GCF of Fractions is 3/271440.Finally, GCF of Fractions for 1575/720, 1209/754 is 3/271440.