GCF of 9977/512, 1198/228
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9977/512, 1198/228 i.e 1/29184 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9977/512, 1198/228.
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 9977/512,1198/228?
Given fractions are 9977/512,1198/228
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 9977/512,1198/228, numerators are 9977,1198
Denominators are 512,228
The GCF of 9977,1198 is 1 .
LCM of 512,228 is 29184.
The greatest common factor of 9977/512,1198/228 = [GCF of 9977,1198]/[LCM of 512,228]= 1/29184
Therefore, the GCF of 9977/512,1198/228 is 1/29184.
To find the highest common factor of 9977,1198, we have to find the factors of both numbers and list the highest common factor.
The factors of 9977 are 1, 11, 907, 9977
The factors of 1198 are 1, 2, 599, 1198
The HCF of 9977,1198 is 1.
Lets's calculate GCF of 9977,1198
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 9977,1198 By Matching Biggest Common Factor Method
Now, list down the factors of 9977
:1,11,907,9977
Now, list down the factors of 1198
:1,2,599,1198
Greatest Common Factor
We found the factors 9977,1198 . The biggest common factor number is the GCF number.
So the greatest common factor 9977,1198 is 1.
Lets's calculate LCM of 512,228
| 2 | 512, 228 |
| 2 | 256, 114 |
| 128, 57 |
∴ So the LCM of the given numbers is 2 x 2 x 128 x 57 = 29184
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/29184
Therefore, the GCF of Fractions 9977/512,1198/228 is 1/29184
Least Common Multiple of 512,228 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 512,228 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(512,228) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(512,228) x common factors =4 x 1 = 4
LCM(512,228) = ( 512 × 228 ) / 4
LCM(512,228) = 116736 / 4
LCM(512,228) = 29184
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FAQs on GCF of Fractions of 9977/512, 1198/228
1. What is the HCF of 9977,1198?
The HCF of 9977,1198 is 1
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 9977/512, 1198/228?
Answer: GCF of Numerators as per given numbers 9977/512, 1198/228 is
GCF of Numerators i.e. for 9977,1198 is 1
LCM of denominators i.e. for 512,228 is 29184.
Thus, GCF of Fractions is 1/29184.Finally, GCF of Fractions for 9977/512, 1198/228 is 1/29184.