GCF of 496/14, 420/384
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 496/14, 420/384 i.e 4/2688 easily. The following is the detailed procedure to determine the greatest common factor of fractions 496/14, 420/384.
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 496/14,420/384?
Given fractions are 496/14,420/384
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 496/14,420/384, numerators are 496,420
Denominators are 14,384
The GCF of 496,420 is 4 .
LCM of 14,384 is 2688.
The greatest common factor of 496/14,420/384 = [GCF of 496,420]/[LCM of 14,384]= 4/2688
Therefore, the GCF of 496/14,420/384 is 4/2688.
To find the highest common factor of 496,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248, 496
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 496,420 is 4.
Lets's calculate GCF of 496,420
| 2 | 496, 420 |
| 2 | 248, 210 |
| 124, 105 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 496,420 By Matching Biggest Common Factor Method
Now, list down the factors of 496
:1,2,4,8,16,31,62,124,248,496
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 496,420 . The biggest common factor number is the GCF number.
So the greatest common factor 496,420 is 4.
Lets's calculate LCM of 14,384
| 2 | 14, 384 |
| 7, 192 |
∴ So the LCM of the given numbers is 2 x 7 x 192 = 2688
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/2688
Therefore, the GCF of Fractions 496/14,420/384 is 4/2688
Least Common Multiple of 14,384 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 14,384 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,384) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(14,384) x common factors =2 x 1 = 2
LCM(14,384) = ( 14 × 384 ) / 2
LCM(14,384) = 5376 / 2
LCM(14,384) = 2688
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 496/14, 420/384
1. What is the HCF of 496,420?
The HCF of 496,420 is 4
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 496/14, 420/384?
Answer: GCF of Numerators as per given numbers 496/14, 420/384 is
GCF of Numerators i.e. for 496,420 is 4
LCM of denominators i.e. for 14,384 is 2688.
Thus, GCF of Fractions is 4/2688.Finally, GCF of Fractions for 496/14, 420/384 is 4/2688.