GCF of 186/102, 403/128
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 186/102, 403/128 i.e 31/6528 easily. The following is the detailed procedure to determine the greatest common factor of fractions 186/102, 403/128.
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 186/102,403/128?
Given fractions are 186/102,403/128
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 186/102,403/128, numerators are 186,403
Denominators are 102,128
The GCF of 186,403 is 31 .
LCM of 102,128 is 6528.
The greatest common factor of 186/102,403/128 = [GCF of 186,403]/[LCM of 102,128]= 31/6528
Therefore, the GCF of 186/102,403/128 is 31/6528.
To find the highest common factor of 186,403, we have to find the factors of both numbers and list the highest common factor.
The factors of 186 are 1, 2, 3, 6, 31, 62, 93, 186
The factors of 403 are 1, 13, 31, 403
The HCF of 186,403 is 31.
Lets's calculate GCF of 186,403
| 31 | 186, 403 |
| 6, 13 |
∴ So the GCF of the given numbers is 31 = 31
Greatest Common Factor of 186,403 By Matching Biggest Common Factor Method
Now, list down the factors of 186
:1,2,3,6,31,62,93,186
Now, list down the factors of 403
:1,13,31,403
Greatest Common Factor
We found the factors 186,403 . The biggest common factor number is the GCF number.
So the greatest common factor 186,403 is 31.
Lets's calculate LCM of 102,128
| 2 | 102, 128 |
| 51, 64 |
∴ So the LCM of the given numbers is 2 x 51 x 64 = 6528
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/6528
Therefore, the GCF of Fractions 186/102,403/128 is 31/6528
Least Common Multiple of 102,128 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 102,128 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(102,128) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(102,128) x common factors =2 x 1 = 2
LCM(102,128) = ( 102 × 128 ) / 2
LCM(102,128) = 13056 / 2
LCM(102,128) = 6528
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FAQs on GCF of Fractions of 186/102, 403/128
1. What is the HCF of 186,403?
The HCF of 186,403 is 31
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 186/102, 403/128?
Answer: GCF of Numerators as per given numbers 186/102, 403/128 is
GCF of Numerators i.e. for 186,403 is 31
LCM of denominators i.e. for 102,128 is 6528.
Thus, GCF of Fractions is 31/6528.Finally, GCF of Fractions for 186/102, 403/128 is 31/6528.