GCF of 494/17, 420/958
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 494/17, 420/958 i.e 2/16286 easily. The following is the detailed procedure to determine the greatest common factor of fractions 494/17, 420/958.
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 494/17,420/958?
Given fractions are 494/17,420/958
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 494/17,420/958, numerators are 494,420
Denominators are 17,958
The GCF of 494,420 is 2 .
LCM of 17,958 is 16286.
The greatest common factor of 494/17,420/958 = [GCF of 494,420]/[LCM of 17,958]= 2/16286
Therefore, the GCF of 494/17,420/958 is 2/16286.
To find the highest common factor of 494,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 494 are 1, 2, 13, 19, 26, 38, 247, 494
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 494,420 is 2.
Lets's calculate GCF of 494,420
| 2 | 494, 420 |
| 247, 210 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 494,420 By Matching Biggest Common Factor Method
Now, list down the factors of 494
:1,2,13,19,26,38,247,494
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 494,420 . The biggest common factor number is the GCF number.
So the greatest common factor 494,420 is 2.
Lets's calculate LCM of 17,958
Given numbers has no common factors except 1. So, there LCM is their product i.e 16286
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/16286
Therefore, the GCF of Fractions 494/17,420/958 is 2/16286
Least Common Multiple of 17,958 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 17,958 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(17,958) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(17,958) x common factors =1 x 1 = 1
LCM(17,958) = ( 17 × 958 ) / 1
LCM(17,958) = 16286 / 1
LCM(17,958) = 16286
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 494/17, 420/958
1. What is the HCF of 494,420?
The HCF of 494,420 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 494/17, 420/958?
Answer: GCF of Numerators as per given numbers 494/17, 420/958 is
GCF of Numerators i.e. for 494,420 is 2
LCM of denominators i.e. for 17,958 is 16286.
Thus, GCF of Fractions is 2/16286.Finally, GCF of Fractions for 494/17, 420/958 is 2/16286.