GCF of 112/380, 398/838
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 112/380, 398/838 i.e 2/159220 easily. The following is the detailed procedure to determine the greatest common factor of fractions 112/380, 398/838.
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 112/380,398/838?
Given fractions are 112/380,398/838
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 112/380,398/838, numerators are 112,398
Denominators are 380,838
The GCF of 112,398 is 2 .
LCM of 380,838 is 159220.
The greatest common factor of 112/380,398/838 = [GCF of 112,398]/[LCM of 380,838]= 2/159220
Therefore, the GCF of 112/380,398/838 is 2/159220.
To find the highest common factor of 112,398, we have to find the factors of both numbers and list the highest common factor.
The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
The factors of 398 are 1, 2, 199, 398
The HCF of 112,398 is 2.
Lets's calculate GCF of 112,398
| 2 | 112, 398 |
| 56, 199 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 112,398 By Matching Biggest Common Factor Method
Now, list down the factors of 112
:1,2,4,7,8,14,16,28,56,112
Now, list down the factors of 398
:1,2,199,398
Greatest Common Factor
We found the factors 112,398 . The biggest common factor number is the GCF number.
So the greatest common factor 112,398 is 2.
Lets's calculate LCM of 380,838
| 2 | 380, 838 |
| 190, 419 |
∴ So the LCM of the given numbers is 2 x 190 x 419 = 159220
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/159220
Therefore, the GCF of Fractions 112/380,398/838 is 2/159220
Least Common Multiple of 380,838 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 380,838 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(380,838) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(380,838) x common factors =2 x 1 = 2
LCM(380,838) = ( 380 × 838 ) / 2
LCM(380,838) = 318440 / 2
LCM(380,838) = 159220
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FAQs on GCF of Fractions of 112/380, 398/838
1. What is the HCF of 112,398?
The HCF of 112,398 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 112/380, 398/838?
Answer: GCF of Numerators as per given numbers 112/380, 398/838 is
GCF of Numerators i.e. for 112,398 is 2
LCM of denominators i.e. for 380,838 is 159220.
Thus, GCF of Fractions is 2/159220.Finally, GCF of Fractions for 112/380, 398/838 is 2/159220.