GCF of 576/107, 720/344
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 576/107, 720/344 i.e 144/36808 easily. The following is the detailed procedure to determine the greatest common factor of fractions 576/107, 720/344.
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 576/107,720/344?
Given fractions are 576/107,720/344
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 576/107,720/344, numerators are 576,720
Denominators are 107,344
The GCF of 576,720 is 144 .
LCM of 107,344 is 36808.
The greatest common factor of 576/107,720/344 = [GCF of 576,720]/[LCM of 107,344]= 144/36808
Therefore, the GCF of 576/107,720/344 is 144/36808.
To find the highest common factor of 576,720, we have to find the factors of both numbers and list the highest common factor.
The factors of 576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576
The factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720
The HCF of 576,720 is 144.
Lets's calculate GCF of 576,720
| 2 | 576, 720 |
| 2 | 288, 360 |
| 2 | 144, 180 |
| 2 | 72, 90 |
| 3 | 36, 45 |
| 3 | 12, 15 |
| 4, 5 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 3 x 3 = 144
Greatest Common Factor of 576,720 By Matching Biggest Common Factor Method
Now, list down the factors of 576
:1,2,3,4,6,8,9,12,16,18,24,32,36,48,64,72,96,144,192,288,576
Now, list down the factors of 720
:1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,36,40,45,48,60,72,80,90,120,144,180,240,360,720
Greatest Common Factor
We found the factors 576,720 . The biggest common factor number is the GCF number.
So the greatest common factor 576,720 is 144.
Lets's calculate LCM of 107,344
Given numbers has no common factors except 1. So, there LCM is their product i.e 36808
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 144/36808
Therefore, the GCF of Fractions 576/107,720/344 is 144/36808
Least Common Multiple of 107,344 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 107,344 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(107,344) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(107,344) x common factors =1 x 1 = 1
LCM(107,344) = ( 107 × 344 ) / 1
LCM(107,344) = 36808 / 1
LCM(107,344) = 36808
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FAQs on GCF of Fractions of 576/107, 720/344
1. What is the HCF of 576,720?
The HCF of 576,720 is 144
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 576/107, 720/344?
Answer: GCF of Numerators as per given numbers 576/107, 720/344 is
GCF of Numerators i.e. for 576,720 is 144
LCM of denominators i.e. for 107,344 is 36808.
Thus, GCF of Fractions is 144/36808.Finally, GCF of Fractions for 576/107, 720/344 is 144/36808.