GCF of 5400/600, 9936/1705
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5400/600, 9936/1705 i.e 216/204600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5400/600, 9936/1705.
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 5400/600,9936/1705?
Given fractions are 5400/600,9936/1705
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 5400/600,9936/1705, numerators are 5400,9936
Denominators are 600,1705
The GCF of 5400,9936 is 216 .
LCM of 600,1705 is 204600.
The greatest common factor of 5400/600,9936/1705 = [GCF of 5400,9936]/[LCM of 600,1705]= 216/204600
Therefore, the GCF of 5400/600,9936/1705 is 216/204600.
To find the highest common factor of 5400,9936, we have to find the factors of both numbers and list the highest common factor.
The factors of 5400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700, 5400
The factors of 9936 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 23, 24, 27, 36, 46, 48, 54, 69, 72, 92, 108, 138, 144, 184, 207, 216, 276, 368, 414, 432, 552, 621, 828, 1104, 1242, 1656, 2484, 3312, 4968, 9936
The HCF of 5400,9936 is 216.
Lets's calculate GCF of 5400,9936
| 2 | 5400, 9936 |
| 2 | 2700, 4968 |
| 2 | 1350, 2484 |
| 3 | 675, 1242 |
| 3 | 225, 414 |
| 3 | 75, 138 |
| 25, 46 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 x 3 x 3 = 216
Greatest Common Factor of 5400,9936 By Matching Biggest Common Factor Method
Now, list down the factors of 5400
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,25,27,30,36,40,45,50,54,60,72,75,90,100,108,120,135,150,180,200,216,225,270,300,360,450,540,600,675,900,1080,1350,1800,2700,5400
Now, list down the factors of 9936
:1,2,3,4,6,8,9,12,16,18,23,24,27,36,46,48,54,69,72,92,108,138,144,184,207,216,276,368,414,432,552,621,828,1104,1242,1656,2484,3312,4968,9936
Greatest Common Factor
We found the factors 5400,9936 . The biggest common factor number is the GCF number.
So the greatest common factor 5400,9936 is 216.
Lets's calculate LCM of 600,1705
| 5 | 600, 1705 |
| 120, 341 |
∴ So the LCM of the given numbers is 5 x 120 x 341 = 204600
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 216/204600
Therefore, the GCF of Fractions 5400/600,9936/1705 is 216/204600
Least Common Multiple of 600,1705 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 600,1705 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(600,1705) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(600,1705) x common factors =5 x 1 = 5
LCM(600,1705) = ( 600 × 1705 ) / 5
LCM(600,1705) = 1023000 / 5
LCM(600,1705) = 204600
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FAQs on GCF of Fractions of 5400/600, 9936/1705
1. What is the HCF of 5400,9936?
The HCF of 5400,9936 is 216
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 5400/600, 9936/1705?
Answer: GCF of Numerators as per given numbers 5400/600, 9936/1705 is
GCF of Numerators i.e. for 5400,9936 is 216
LCM of denominators i.e. for 600,1705 is 204600.
Thus, GCF of Fractions is 216/204600.Finally, GCF of Fractions for 5400/600, 9936/1705 is 216/204600.