GCF of 724/800, 210/180
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 724/800, 210/180 i.e 2/7200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 724/800, 210/180.
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 724/800,210/180?
Given fractions are 724/800,210/180
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 724/800,210/180, numerators are 724,210
Denominators are 800,180
The GCF of 724,210 is 2 .
LCM of 800,180 is 7200.
The greatest common factor of 724/800,210/180 = [GCF of 724,210]/[LCM of 800,180]= 2/7200
Therefore, the GCF of 724/800,210/180 is 2/7200.
To find the highest common factor of 724,210, we have to find the factors of both numbers and list the highest common factor.
The factors of 724 are 1, 2, 4, 181, 362, 724
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The HCF of 724,210 is 2.
Lets's calculate GCF of 724,210
| 2 | 724, 210 |
| 362, 105 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 724,210 By Matching Biggest Common Factor Method
Now, list down the factors of 724
:1,2,4,181,362,724
Now, list down the factors of 210
:1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
Greatest Common Factor
We found the factors 724,210 . The biggest common factor number is the GCF number.
So the greatest common factor 724,210 is 2.
Lets's calculate LCM of 800,180
| 2 | 800, 180 |
| 2 | 400, 90 |
| 5 | 200, 45 |
| 40, 9 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 40 x 9 = 7200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/7200
Therefore, the GCF of Fractions 724/800,210/180 is 2/7200
Least Common Multiple of 800,180 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 800,180 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(800,180) = 20
common factors(in case of two or more numbers have common factors) = 1
GCF(800,180) x common factors =20 x 1 = 20
LCM(800,180) = ( 800 × 180 ) / 20
LCM(800,180) = 144000 / 20
LCM(800,180) = 7200
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FAQs on GCF of Fractions of 724/800, 210/180
1. What is the HCF of 724,210?
The HCF of 724,210 is 2
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 724/800, 210/180?
Answer: GCF of Numerators as per given numbers 724/800, 210/180 is
GCF of Numerators i.e. for 724,210 is 2
LCM of denominators i.e. for 800,180 is 7200.
Thus, GCF of Fractions is 2/7200.Finally, GCF of Fractions for 724/800, 210/180 is 2/7200.