GCF of 7200/454, 1917/432
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7200/454, 1917/432 i.e 9/98064 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7200/454, 1917/432.
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 7200/454,1917/432?
Given fractions are 7200/454,1917/432
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 7200/454,1917/432, numerators are 7200,1917
Denominators are 454,432
The GCF of 7200,1917 is 9 .
LCM of 454,432 is 98064.
The greatest common factor of 7200/454,1917/432 = [GCF of 7200,1917]/[LCM of 454,432]= 9/98064
Therefore, the GCF of 7200/454,1917/432 is 9/98064.
To find the highest common factor of 7200,1917, 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 1917 are 1, 3, 9, 27, 71, 213, 639, 1917
The HCF of 7200,1917 is 9.
Lets's calculate GCF of 7200,1917
| 3 | 7200, 1917 |
| 3 | 2400, 639 |
| 800, 213 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 7200,1917 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 1917
:1,3,9,27,71,213,639,1917
Greatest Common Factor
We found the factors 7200,1917 . The biggest common factor number is the GCF number.
So the greatest common factor 7200,1917 is 9.
Lets's calculate LCM of 454,432
| 2 | 454, 432 |
| 227, 216 |
∴ So the LCM of the given numbers is 2 x 227 x 216 = 98064
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/98064
Therefore, the GCF of Fractions 7200/454,1917/432 is 9/98064
Least Common Multiple of 454,432 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 454,432 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(454,432) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(454,432) x common factors =2 x 1 = 2
LCM(454,432) = ( 454 × 432 ) / 2
LCM(454,432) = 196128 / 2
LCM(454,432) = 98064
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FAQs on GCF of Fractions of 7200/454, 1917/432
1. What is the HCF of 7200,1917?
The HCF of 7200,1917 is 9
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 7200/454, 1917/432?
Answer: GCF of Numerators as per given numbers 7200/454, 1917/432 is
GCF of Numerators i.e. for 7200,1917 is 9
LCM of denominators i.e. for 454,432 is 98064.
Thus, GCF of Fractions is 9/98064.Finally, GCF of Fractions for 7200/454, 1917/432 is 9/98064.