GCF of 7200/623, 3000/261
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7200/623, 3000/261 i.e 600/162603 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7200/623, 3000/261.
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 7200/623,3000/261?
Given fractions are 7200/623,3000/261
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 7200/623,3000/261, numerators are 7200,3000
Denominators are 623,261
The GCF of 7200,3000 is 600 .
LCM of 623,261 is 162603.
The greatest common factor of 7200/623,3000/261 = [GCF of 7200,3000]/[LCM of 623,261]= 600/162603
Therefore, the GCF of 7200/623,3000/261 is 600/162603.
To find the highest common factor of 7200,3000, we have to find the factors of both numbers and list the highest common factor.
The factors of 7200 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 96, 100, 120, 144, 150, 160, 180, 200, 225, 240, 288, 300, 360, 400, 450, 480, 600, 720, 800, 900, 1200, 1440, 1800, 2400, 3600, 7200
The factors of 3000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 125, 150, 200, 250, 300, 375, 500, 600, 750, 1000, 1500, 3000
The HCF of 7200,3000 is 600.
Lets's calculate GCF of 7200,3000
| 2 | 7200, 3000 |
| 2 | 3600, 1500 |
| 2 | 1800, 750 |
| 3 | 900, 375 |
| 5 | 300, 125 |
| 5 | 60, 25 |
| 12, 5 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 x 5 x 5 = 600
Greatest Common Factor of 7200,3000 By Matching Biggest Common Factor Method
Now, list down the factors of 7200
:1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,30,32,36,40,45,48,50,60,72,75,80,90,96,100,120,144,150,160,180,200,225,240,288,300,360,400,450,480,600,720,800,900,1200,1440,1800,2400,3600,7200
Now, list down the factors of 3000
:1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,125,150,200,250,300,375,500,600,750,1000,1500,3000
Greatest Common Factor
We found the factors 7200,3000 . The biggest common factor number is the GCF number.
So the greatest common factor 7200,3000 is 600.
Lets's calculate LCM of 623,261
Given numbers has no common factors except 1. So, there LCM is their product i.e 162603
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 600/162603
Therefore, the GCF of Fractions 7200/623,3000/261 is 600/162603
Least Common Multiple of 623,261 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 623,261 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(623,261) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(623,261) x common factors =1 x 1 = 1
LCM(623,261) = ( 623 × 261 ) / 1
LCM(623,261) = 162603 / 1
LCM(623,261) = 162603
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FAQs on GCF of Fractions of 7200/623, 3000/261
1. What is the HCF of 7200,3000?
The HCF of 7200,3000 is 600
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 7200/623, 3000/261?
Answer: GCF of Numerators as per given numbers 7200/623, 3000/261 is
GCF of Numerators i.e. for 7200,3000 is 600
LCM of denominators i.e. for 623,261 is 162603.
Thus, GCF of Fractions is 600/162603.Finally, GCF of Fractions for 7200/623, 3000/261 is 600/162603.