GCF of 500/123, 4182/257
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 500/123, 4182/257 i.e 2/31611 easily. The following is the detailed procedure to determine the greatest common factor of fractions 500/123, 4182/257.
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 500/123,4182/257?
Given fractions are 500/123,4182/257
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 500/123,4182/257, numerators are 500,4182
Denominators are 123,257
The GCF of 500,4182 is 2 .
LCM of 123,257 is 31611.
The greatest common factor of 500/123,4182/257 = [GCF of 500,4182]/[LCM of 123,257]= 2/31611
Therefore, the GCF of 500/123,4182/257 is 2/31611.
To find the highest common factor of 500,4182, we have to find the factors of both numbers and list the highest common factor.
The factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
The factors of 4182 are 1, 2, 3, 6, 17, 34, 41, 51, 82, 102, 123, 246, 697, 1394, 2091, 4182
The HCF of 500,4182 is 2.
Lets's calculate GCF of 500,4182
| 2 | 500, 4182 |
| 250, 2091 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 500,4182 By Matching Biggest Common Factor Method
Now, list down the factors of 500
:1,2,4,5,10,20,25,50,100,125,250,500
Now, list down the factors of 4182
:1,2,3,6,17,34,41,51,82,102,123,246,697,1394,2091,4182
Greatest Common Factor
We found the factors 500,4182 . The biggest common factor number is the GCF number.
So the greatest common factor 500,4182 is 2.
Lets's calculate LCM of 123,257
Given numbers has no common factors except 1. So, there LCM is their product i.e 31611
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/31611
Therefore, the GCF of Fractions 500/123,4182/257 is 2/31611
Least Common Multiple of 123,257 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 123,257 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(123,257) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(123,257) x common factors =1 x 1 = 1
LCM(123,257) = ( 123 × 257 ) / 1
LCM(123,257) = 31611 / 1
LCM(123,257) = 31611
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FAQs on GCF of Fractions of 500/123, 4182/257
1. What is the HCF of 500,4182?
The HCF of 500,4182 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 500/123, 4182/257?
Answer: GCF of Numerators as per given numbers 500/123, 4182/257 is
GCF of Numerators i.e. for 500,4182 is 2
LCM of denominators i.e. for 123,257 is 31611.
Thus, GCF of Fractions is 2/31611.Finally, GCF of Fractions for 500/123, 4182/257 is 2/31611.