GCF of 1728/158, 9738/8464
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1728/158, 9738/8464 i.e 18/668656 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1728/158, 9738/8464.
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 1728/158,9738/8464?
Given fractions are 1728/158,9738/8464
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 1728/158,9738/8464, numerators are 1728,9738
Denominators are 158,8464
The GCF of 1728,9738 is 18 .
LCM of 158,8464 is 668656.
The greatest common factor of 1728/158,9738/8464 = [GCF of 1728,9738]/[LCM of 158,8464]= 18/668656
Therefore, the GCF of 1728/158,9738/8464 is 18/668656.
To find the highest common factor of 1728,9738, 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 9738 are 1, 2, 3, 6, 9, 18, 541, 1082, 1623, 3246, 4869, 9738
The HCF of 1728,9738 is 18.
Lets's calculate GCF of 1728,9738
| 2 | 1728, 9738 |
| 3 | 864, 4869 |
| 3 | 288, 1623 |
| 96, 541 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 1728,9738 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 9738
:1,2,3,6,9,18,541,1082,1623,3246,4869,9738
Greatest Common Factor
We found the factors 1728,9738 . The biggest common factor number is the GCF number.
So the greatest common factor 1728,9738 is 18.
Lets's calculate LCM of 158,8464
| 2 | 158, 8464 |
| 79, 4232 |
∴ So the LCM of the given numbers is 2 x 79 x 4232 = 668656
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/668656
Therefore, the GCF of Fractions 1728/158,9738/8464 is 18/668656
Least Common Multiple of 158,8464 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 158,8464 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(158,8464) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(158,8464) x common factors =2 x 1 = 2
LCM(158,8464) = ( 158 × 8464 ) / 2
LCM(158,8464) = 1337312 / 2
LCM(158,8464) = 668656
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FAQs on GCF of Fractions of 1728/158, 9738/8464
1. What is the HCF of 1728,9738?
The HCF of 1728,9738 is 18
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 1728/158, 9738/8464?
Answer: GCF of Numerators as per given numbers 1728/158, 9738/8464 is
GCF of Numerators i.e. for 1728,9738 is 18
LCM of denominators i.e. for 158,8464 is 668656.
Thus, GCF of Fractions is 18/668656.Finally, GCF of Fractions for 1728/158, 9738/8464 is 18/668656.