GCF of 418/230, 1727/345
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 418/230, 1727/345 i.e 11/690 easily. The following is the detailed procedure to determine the greatest common factor of fractions 418/230, 1727/345.
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 418/230,1727/345?
Given fractions are 418/230,1727/345
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 418/230,1727/345, numerators are 418,1727
Denominators are 230,345
The GCF of 418,1727 is 11 .
LCM of 230,345 is 690.
The greatest common factor of 418/230,1727/345 = [GCF of 418,1727]/[LCM of 230,345]= 11/690
Therefore, the GCF of 418/230,1727/345 is 11/690.
To find the highest common factor of 418,1727, we have to find the factors of both numbers and list the highest common factor.
The factors of 418 are 1, 2, 11, 19, 22, 38, 209, 418
The factors of 1727 are 1, 11, 157, 1727
The HCF of 418,1727 is 11.
Lets's calculate GCF of 418,1727
| 11 | 418, 1727 |
| 38, 157 |
∴ So the GCF of the given numbers is 11 = 11
Greatest Common Factor of 418,1727 By Matching Biggest Common Factor Method
Now, list down the factors of 418
:1,2,11,19,22,38,209,418
Now, list down the factors of 1727
:1,11,157,1727
Greatest Common Factor
We found the factors 418,1727 . The biggest common factor number is the GCF number.
So the greatest common factor 418,1727 is 11.
Lets's calculate LCM of 230,345
| 5 | 230, 345 |
| 23 | 46, 69 |
| 2, 3 |
∴ So the LCM of the given numbers is 5 x 23 x 2 x 3 = 690
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/690
Therefore, the GCF of Fractions 418/230,1727/345 is 11/690
Least Common Multiple of 230,345 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 230,345 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(230,345) = 115
common factors(in case of two or more numbers have common factors) = 1
GCF(230,345) x common factors =115 x 1 = 115
LCM(230,345) = ( 230 × 345 ) / 115
LCM(230,345) = 79350 / 115
LCM(230,345) = 690
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FAQs on GCF of Fractions of 418/230, 1727/345
1. What is the HCF of 418,1727?
The HCF of 418,1727 is 11
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 418/230, 1727/345?
Answer: GCF of Numerators as per given numbers 418/230, 1727/345 is
GCF of Numerators i.e. for 418,1727 is 11
LCM of denominators i.e. for 230,345 is 690.
Thus, GCF of Fractions is 11/690.Finally, GCF of Fractions for 418/230, 1727/345 is 11/690.