GCF of 231/51, 282/413
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 231/51, 282/413 i.e 3/21063 easily. The following is the detailed procedure to determine the greatest common factor of fractions 231/51, 282/413.
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 231/51,282/413?
Given fractions are 231/51,282/413
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 231/51,282/413, numerators are 231,282
Denominators are 51,413
The GCF of 231,282 is 3 .
LCM of 51,413 is 21063.
The greatest common factor of 231/51,282/413 = [GCF of 231,282]/[LCM of 51,413]= 3/21063
Therefore, the GCF of 231/51,282/413 is 3/21063.
To find the highest common factor of 231,282, we have to find the factors of both numbers and list the highest common factor.
The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231
The factors of 282 are 1, 2, 3, 6, 47, 94, 141, 282
The HCF of 231,282 is 3.
Lets's calculate GCF of 231,282
| 3 | 231, 282 |
| 77, 94 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 231,282 By Matching Biggest Common Factor Method
Now, list down the factors of 231
:1,3,7,11,21,33,77,231
Now, list down the factors of 282
:1,2,3,6,47,94,141,282
Greatest Common Factor
We found the factors 231,282 . The biggest common factor number is the GCF number.
So the greatest common factor 231,282 is 3.
Lets's calculate LCM of 51,413
Given numbers has no common factors except 1. So, there LCM is their product i.e 21063
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/21063
Therefore, the GCF of Fractions 231/51,282/413 is 3/21063
Least Common Multiple of 51,413 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 51,413 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,413) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(51,413) x common factors =1 x 1 = 1
LCM(51,413) = ( 51 × 413 ) / 1
LCM(51,413) = 21063 / 1
LCM(51,413) = 21063
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FAQs on GCF of Fractions of 231/51, 282/413
1. What is the HCF of 231,282?
The HCF of 231,282 is 3
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 231/51, 282/413?
Answer: GCF of Numerators as per given numbers 231/51, 282/413 is
GCF of Numerators i.e. for 231,282 is 3
LCM of denominators i.e. for 51,413 is 21063.
Thus, GCF of Fractions is 3/21063.Finally, GCF of Fractions for 231/51, 282/413 is 3/21063.