GCF of 195/54, 744/686
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 195/54, 744/686 i.e 3/18522 easily. The following is the detailed procedure to determine the greatest common factor of fractions 195/54, 744/686.
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 195/54,744/686?
Given fractions are 195/54,744/686
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 195/54,744/686, numerators are 195,744
Denominators are 54,686
The GCF of 195,744 is 3 .
LCM of 54,686 is 18522.
The greatest common factor of 195/54,744/686 = [GCF of 195,744]/[LCM of 54,686]= 3/18522
Therefore, the GCF of 195/54,744/686 is 3/18522.
To find the highest common factor of 195,744, we have to find the factors of both numbers and list the highest common factor.
The factors of 195 are 1, 3, 5, 13, 15, 39, 65, 195
The factors of 744 are 1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 124, 186, 248, 372, 744
The HCF of 195,744 is 3.
Lets's calculate GCF of 195,744
| 3 | 195, 744 |
| 65, 248 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 195,744 By Matching Biggest Common Factor Method
Now, list down the factors of 195
:1,3,5,13,15,39,65,195
Now, list down the factors of 744
:1,2,3,4,6,8,12,24,31,62,93,124,186,248,372,744
Greatest Common Factor
We found the factors 195,744 . The biggest common factor number is the GCF number.
So the greatest common factor 195,744 is 3.
Lets's calculate LCM of 54,686
| 2 | 54, 686 |
| 27, 343 |
∴ So the LCM of the given numbers is 2 x 27 x 343 = 18522
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/18522
Therefore, the GCF of Fractions 195/54,744/686 is 3/18522
Least Common Multiple of 54,686 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 54,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,686) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(54,686) x common factors =2 x 1 = 2
LCM(54,686) = ( 54 × 686 ) / 2
LCM(54,686) = 37044 / 2
LCM(54,686) = 18522
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FAQs on GCF of Fractions of 195/54, 744/686
1. What is the HCF of 195,744?
The HCF of 195,744 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 195/54, 744/686?
Answer: GCF of Numerators as per given numbers 195/54, 744/686 is
GCF of Numerators i.e. for 195,744 is 3
LCM of denominators i.e. for 54,686 is 18522.
Thus, GCF of Fractions is 3/18522.Finally, GCF of Fractions for 195/54, 744/686 is 3/18522.