GCF of 723/75, 360/4314
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 723/75, 360/4314 i.e 3/107850 easily. The following is the detailed procedure to determine the greatest common factor of fractions 723/75, 360/4314.
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 723/75,360/4314?
Given fractions are 723/75,360/4314
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 723/75,360/4314, numerators are 723,360
Denominators are 75,4314
The GCF of 723,360 is 3 .
LCM of 75,4314 is 107850.
The greatest common factor of 723/75,360/4314 = [GCF of 723,360]/[LCM of 75,4314]= 3/107850
Therefore, the GCF of 723/75,360/4314 is 3/107850.
To find the highest common factor of 723,360, we have to find the factors of both numbers and list the highest common factor.
The factors of 723 are 1, 3, 241, 723
The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
The HCF of 723,360 is 3.
Lets's calculate GCF of 723,360
| 3 | 723, 360 |
| 241, 120 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 723,360 By Matching Biggest Common Factor Method
Now, list down the factors of 723
:1,3,241,723
Now, list down the factors of 360
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360
Greatest Common Factor
We found the factors 723,360 . The biggest common factor number is the GCF number.
So the greatest common factor 723,360 is 3.
Lets's calculate LCM of 75,4314
| 3 | 75, 4314 |
| 25, 1438 |
∴ So the LCM of the given numbers is 3 x 25 x 1438 = 107850
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/107850
Therefore, the GCF of Fractions 723/75,360/4314 is 3/107850
Least Common Multiple of 75,4314 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 75,4314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,4314) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(75,4314) x common factors =3 x 1 = 3
LCM(75,4314) = ( 75 × 4314 ) / 3
LCM(75,4314) = 323550 / 3
LCM(75,4314) = 107850
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FAQs on GCF of Fractions of 723/75, 360/4314
1. What is the HCF of 723,360?
The HCF of 723,360 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 723/75, 360/4314?
Answer: GCF of Numerators as per given numbers 723/75, 360/4314 is
GCF of Numerators i.e. for 723,360 is 3
LCM of denominators i.e. for 75,4314 is 107850.
Thus, GCF of Fractions is 3/107850.Finally, GCF of Fractions for 723/75, 360/4314 is 3/107850.