GCF of 1749/491, 3186/5738
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1749/491, 3186/5738 i.e 3/2817358 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1749/491, 3186/5738.
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 1749/491,3186/5738?
Given fractions are 1749/491,3186/5738
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 1749/491,3186/5738, numerators are 1749,3186
Denominators are 491,5738
The GCF of 1749,3186 is 3 .
LCM of 491,5738 is 2817358.
The greatest common factor of 1749/491,3186/5738 = [GCF of 1749,3186]/[LCM of 491,5738]= 3/2817358
Therefore, the GCF of 1749/491,3186/5738 is 3/2817358.
To find the highest common factor of 1749,3186, we have to find the factors of both numbers and list the highest common factor.
The factors of 1749 are 1, 3, 11, 33, 53, 159, 583, 1749
The factors of 3186 are 1, 2, 3, 6, 9, 18, 27, 54, 59, 118, 177, 354, 531, 1062, 1593, 3186
The HCF of 1749,3186 is 3.
Lets's calculate GCF of 1749,3186
| 3 | 1749, 3186 |
| 583, 1062 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 1749,3186 By Matching Biggest Common Factor Method
Now, list down the factors of 1749
:1,3,11,33,53,159,583,1749
Now, list down the factors of 3186
:1,2,3,6,9,18,27,54,59,118,177,354,531,1062,1593,3186
Greatest Common Factor
We found the factors 1749,3186 . The biggest common factor number is the GCF number.
So the greatest common factor 1749,3186 is 3.
Lets's calculate LCM of 491,5738
Given numbers has no common factors except 1. So, there LCM is their product i.e 2817358
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/2817358
Therefore, the GCF of Fractions 1749/491,3186/5738 is 3/2817358
Least Common Multiple of 491,5738 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 491,5738 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(491,5738) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(491,5738) x common factors =1 x 1 = 1
LCM(491,5738) = ( 491 × 5738 ) / 1
LCM(491,5738) = 2817358 / 1
LCM(491,5738) = 2817358
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FAQs on GCF of Fractions of 1749/491, 3186/5738
1. What is the HCF of 1749,3186?
The HCF of 1749,3186 is 3
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 1749/491, 3186/5738?
Answer: GCF of Numerators as per given numbers 1749/491, 3186/5738 is
GCF of Numerators i.e. for 1749,3186 is 3
LCM of denominators i.e. for 491,5738 is 2817358.
Thus, GCF of Fractions is 3/2817358.Finally, GCF of Fractions for 1749/491, 3186/5738 is 3/2817358.