GCF of 992/59, 523/40, 498/16
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 992/59, 523/40, 498/16 i.e 1/4720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 992/59, 523/40, 498/16.
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 992/59,523/40,498/16?
Given fractions are 992/59,523/40,498/16
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 992/59,523/40,498/16, numerators are 992,523,498
Denominators are 59,40,16
The GCF of 992,523,498 is 1 .
LCM of 59,40,16 is 4720.
The greatest common factor of 992/59,523/40,498/16 = [GCF of 992,523,498]/[LCM of 59,40,16]= 1/4720
Therefore, the GCF of 992/59,523/40,498/16 is 1/4720.
To find the highest common factor of 992,523,498, we have to find the factors of both numbers and list the highest common factor.
The factors of 992 are 1, 2, 4, 8, 16, 31, 32, 62, 124, 248, 496, 992
The factors of 523 are 1, 523
The factors of 498 are 1, 2, 3, 6, 83, 166, 249, 498
The HCF of 992,523,498 is 1.
Lets's calculate GCF of 992,523,498
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 992,523,498 By Matching Biggest Common Factor Method
Now, list down the factors of 992
:1,2,4,8,16,31,32,62,124,248,496,992
Now, list down the factors of 523
:1,523
Now, list down the factors of 498
:1,2,3,6,83,166,249,498
Greatest Common Factor
We found the factors 992,523,498 . The biggest common factor number is the GCF number.
So the greatest common factor 992,523,498 is 1.
Lets's calculate LCM of 59,40,16
| 2 | 59, 40, 16 |
| 2 | 59, 20, 8 |
| 2 | 59, 10, 4 |
| 59, 5, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 59 x 5 x 2 = 4720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4720
Therefore, the GCF of Fractions 992/59,523/40,498/16 is 1/4720
Least Common Multiple of 59,40,16 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 59,40,16 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(59,40,16) = 1
common factors(in case of two or more numbers have common factors) = 8
GCF(59,40,16) x common factors =1 x 8 = 8
LCM(59,40,16) = ( 59 × 40 × 16 ) / 8
LCM(59,40,16) = 37760 / 8
LCM(59,40,16) = 4720
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 992/59, 523/40, 498/16
1. What is the HCF of 992,523,498?
The HCF of 992,523,498 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 992/59, 523/40, 498/16?
Answer: GCF of Numerators as per given numbers 992/59, 523/40, 498/16 is
GCF of Numerators i.e. for 992,523,498 is 1
LCM of denominators i.e. for 59,40,16 is 4720.
Thus, GCF of Fractions is 1/4720.Finally, GCF of Fractions for 992/59, 523/40, 498/16 is 1/4720.