GCF of 40/23, 198/48, 420/199
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 40/23, 198/48, 420/199 i.e 2/219696 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/23, 198/48, 420/199.
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 40/23,198/48,420/199?
Given fractions are 40/23,198/48,420/199
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 40/23,198/48,420/199, numerators are 40,198,420
Denominators are 23,48,199
The GCF of 40,198,420 is 2 .
LCM of 23,48,199 is 219696.
The greatest common factor of 40/23,198/48,420/199 = [GCF of 40,198,420]/[LCM of 23,48,199]= 2/219696
Therefore, the GCF of 40/23,198/48,420/199 is 2/219696.
To find the highest common factor of 40,198,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 40,198,420 is 2.
Lets's calculate GCF of 40,198,420
| 2 | 40, 198, 420 |
| 20, 99, 210 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 40,198,420 By Matching Biggest Common Factor Method
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 198
:1,2,3,6,9,11,18,22,33,66,99,198
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 40,198,420 . The biggest common factor number is the GCF number.
So the greatest common factor 40,198,420 is 2.
Lets's calculate LCM of 23,48,199
Given numbers has no common factors except 1. So, there LCM is their product i.e 219696
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/219696
Therefore, the GCF of Fractions 40/23,198/48,420/199 is 2/219696
Least Common Multiple of 23,48,199 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 23,48,199 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(23,48,199) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(23,48,199) x common factors =1 x 1 = 1
LCM(23,48,199) = ( 23 × 48 × 199 ) / 1
LCM(23,48,199) = 219696 / 1
LCM(23,48,199) = 219696
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FAQs on GCF of Fractions of 40/23, 198/48, 420/199
1. What is the HCF of 40,198,420?
The HCF of 40,198,420 is 2
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 40/23, 198/48, 420/199?
Answer: GCF of Numerators as per given numbers 40/23, 198/48, 420/199 is
GCF of Numerators i.e. for 40,198,420 is 2
LCM of denominators i.e. for 23,48,199 is 219696.
Thus, GCF of Fractions is 2/219696.Finally, GCF of Fractions for 40/23, 198/48, 420/199 is 2/219696.