GCF of 423/72, 513/586
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 423/72, 513/586 i.e 9/21096 easily. The following is the detailed procedure to determine the greatest common factor of fractions 423/72, 513/586.
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 423/72,513/586?
Given fractions are 423/72,513/586
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 423/72,513/586, numerators are 423,513
Denominators are 72,586
The GCF of 423,513 is 9 .
LCM of 72,586 is 21096.
The greatest common factor of 423/72,513/586 = [GCF of 423,513]/[LCM of 72,586]= 9/21096
Therefore, the GCF of 423/72,513/586 is 9/21096.
To find the highest common factor of 423,513, we have to find the factors of both numbers and list the highest common factor.
The factors of 423 are 1, 3, 9, 47, 141, 423
The factors of 513 are 1, 3, 9, 19, 27, 57, 171, 513
The HCF of 423,513 is 9.
Lets's calculate GCF of 423,513
| 3 | 423, 513 |
| 3 | 141, 171 |
| 47, 57 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 423,513 By Matching Biggest Common Factor Method
Now, list down the factors of 423
:1,3,9,47,141,423
Now, list down the factors of 513
:1,3,9,19,27,57,171,513
Greatest Common Factor
We found the factors 423,513 . The biggest common factor number is the GCF number.
So the greatest common factor 423,513 is 9.
Lets's calculate LCM of 72,586
| 2 | 72, 586 |
| 36, 293 |
∴ So the LCM of the given numbers is 2 x 36 x 293 = 21096
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/21096
Therefore, the GCF of Fractions 423/72,513/586 is 9/21096
Least Common Multiple of 72,586 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 72,586 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(72,586) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(72,586) x common factors =2 x 1 = 2
LCM(72,586) = ( 72 × 586 ) / 2
LCM(72,586) = 42192 / 2
LCM(72,586) = 21096
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 423/72, 513/586
1. What is the HCF of 423,513?
The HCF of 423,513 is 9
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 423/72, 513/586?
Answer: GCF of Numerators as per given numbers 423/72, 513/586 is
GCF of Numerators i.e. for 423,513 is 9
LCM of denominators i.e. for 72,586 is 21096.
Thus, GCF of Fractions is 9/21096.Finally, GCF of Fractions for 423/72, 513/586 is 9/21096.