GCF of 403/82, 232/5312
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 403/82, 232/5312 i.e 1/217792 easily. The following is the detailed procedure to determine the greatest common factor of fractions 403/82, 232/5312.
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 403/82,232/5312?
Given fractions are 403/82,232/5312
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 403/82,232/5312, numerators are 403,232
Denominators are 82,5312
The GCF of 403,232 is 1 .
LCM of 82,5312 is 217792.
The greatest common factor of 403/82,232/5312 = [GCF of 403,232]/[LCM of 82,5312]= 1/217792
Therefore, the GCF of 403/82,232/5312 is 1/217792.
To find the highest common factor of 403,232, we have to find the factors of both numbers and list the highest common factor.
The factors of 403 are 1, 13, 31, 403
The factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232
The HCF of 403,232 is 1.
Lets's calculate GCF of 403,232
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 403,232 By Matching Biggest Common Factor Method
Now, list down the factors of 403
:1,13,31,403
Now, list down the factors of 232
:1,2,4,8,29,58,116,232
Greatest Common Factor
We found the factors 403,232 . The biggest common factor number is the GCF number.
So the greatest common factor 403,232 is 1.
Lets's calculate LCM of 82,5312
| 2 | 82, 5312 |
| 41, 2656 |
∴ So the LCM of the given numbers is 2 x 41 x 2656 = 217792
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/217792
Therefore, the GCF of Fractions 403/82,232/5312 is 1/217792
Least Common Multiple of 82,5312 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 82,5312 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,5312) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(82,5312) x common factors =2 x 1 = 2
LCM(82,5312) = ( 82 × 5312 ) / 2
LCM(82,5312) = 435584 / 2
LCM(82,5312) = 217792
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FAQs on GCF of Fractions of 403/82, 232/5312
1. What is the HCF of 403,232?
The HCF of 403,232 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 403/82, 232/5312?
Answer: GCF of Numerators as per given numbers 403/82, 232/5312 is
GCF of Numerators i.e. for 403,232 is 1
LCM of denominators i.e. for 82,5312 is 217792.
Thus, GCF of Fractions is 1/217792.Finally, GCF of Fractions for 403/82, 232/5312 is 1/217792.