GCF of 1728/142, 1951/984
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1728/142, 1951/984 i.e 1/69864 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1728/142, 1951/984.
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 1728/142,1951/984?
Given fractions are 1728/142,1951/984
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 1728/142,1951/984, numerators are 1728,1951
Denominators are 142,984
The GCF of 1728,1951 is 1 .
LCM of 142,984 is 69864.
The greatest common factor of 1728/142,1951/984 = [GCF of 1728,1951]/[LCM of 142,984]= 1/69864
Therefore, the GCF of 1728/142,1951/984 is 1/69864.
To find the highest common factor of 1728,1951, we have to find the factors of both numbers and list the highest common factor.
The factors of 1728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728
The factors of 1951 are 1, 1951
The HCF of 1728,1951 is 1.
Lets's calculate GCF of 1728,1951
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1728,1951 By Matching Biggest Common Factor Method
Now, list down the factors of 1728
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,64,72,96,108,144,192,216,288,432,576,864,1728
Now, list down the factors of 1951
:1,1951
Greatest Common Factor
We found the factors 1728,1951 . The biggest common factor number is the GCF number.
So the greatest common factor 1728,1951 is 1.
Lets's calculate LCM of 142,984
| 2 | 142, 984 |
| 71, 492 |
∴ So the LCM of the given numbers is 2 x 71 x 492 = 69864
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/69864
Therefore, the GCF of Fractions 1728/142,1951/984 is 1/69864
Least Common Multiple of 142,984 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 142,984 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(142,984) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(142,984) x common factors =2 x 1 = 2
LCM(142,984) = ( 142 × 984 ) / 2
LCM(142,984) = 139728 / 2
LCM(142,984) = 69864
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 1728/142, 1951/984
1. What is the HCF of 1728,1951?
The HCF of 1728,1951 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 1728/142, 1951/984?
Answer: GCF of Numerators as per given numbers 1728/142, 1951/984 is
GCF of Numerators i.e. for 1728,1951 is 1
LCM of denominators i.e. for 142,984 is 69864.
Thus, GCF of Fractions is 1/69864.Finally, GCF of Fractions for 1728/142, 1951/984 is 1/69864.