GCF of 2300/111, 8400/9838
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2300/111, 8400/9838 i.e 100/1092018 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2300/111, 8400/9838.
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 2300/111,8400/9838?
Given fractions are 2300/111,8400/9838
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 2300/111,8400/9838, numerators are 2300,8400
Denominators are 111,9838
The GCF of 2300,8400 is 100 .
LCM of 111,9838 is 1092018.
The greatest common factor of 2300/111,8400/9838 = [GCF of 2300,8400]/[LCM of 111,9838]= 100/1092018
Therefore, the GCF of 2300/111,8400/9838 is 100/1092018.
To find the highest common factor of 2300,8400, we have to find the factors of both numbers and list the highest common factor.
The factors of 2300 are 1, 2, 4, 5, 10, 20, 23, 25, 46, 50, 92, 100, 115, 230, 460, 575, 1150, 2300
The factors of 8400 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 140, 150, 168, 175, 200, 210, 240, 280, 300, 336, 350, 400, 420, 525, 560, 600, 700, 840, 1050, 1200, 1400, 1680, 2100, 2800, 4200, 8400
The HCF of 2300,8400 is 100.
Lets's calculate GCF of 2300,8400
| 2 | 2300, 8400 |
| 2 | 1150, 4200 |
| 5 | 575, 2100 |
| 5 | 115, 420 |
| 23, 84 |
∴ So the GCF of the given numbers is 2 x 2 x 5 x 5 = 100
Greatest Common Factor of 2300,8400 By Matching Biggest Common Factor Method
Now, list down the factors of 2300
:1,2,4,5,10,20,23,25,46,50,92,100,115,230,460,575,1150,2300
Now, list down the factors of 8400
:1,2,3,4,5,6,7,8,10,12,14,15,16,20,21,24,25,28,30,35,40,42,48,50,56,60,70,75,80,84,100,105,112,120,140,150,168,175,200,210,240,280,300,336,350,400,420,525,560,600,700,840,1050,1200,1400,1680,2100,2800,4200,8400
Greatest Common Factor
We found the factors 2300,8400 . The biggest common factor number is the GCF number.
So the greatest common factor 2300,8400 is 100.
Lets's calculate LCM of 111,9838
Given numbers has no common factors except 1. So, there LCM is their product i.e 1092018
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 100/1092018
Therefore, the GCF of Fractions 2300/111,8400/9838 is 100/1092018
Least Common Multiple of 111,9838 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 111,9838 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(111,9838) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(111,9838) x common factors =1 x 1 = 1
LCM(111,9838) = ( 111 × 9838 ) / 1
LCM(111,9838) = 1092018 / 1
LCM(111,9838) = 1092018
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FAQs on GCF of Fractions of 2300/111, 8400/9838
1. What is the HCF of 2300,8400?
The HCF of 2300,8400 is 100
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 2300/111, 8400/9838?
Answer: GCF of Numerators as per given numbers 2300/111, 8400/9838 is
GCF of Numerators i.e. for 2300,8400 is 100
LCM of denominators i.e. for 111,9838 is 1092018.
Thus, GCF of Fractions is 100/1092018.Finally, GCF of Fractions for 2300/111, 8400/9838 is 100/1092018.