GCF of 585/414, 346/720
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 585/414, 346/720 i.e 1/16560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 585/414, 346/720.
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 585/414,346/720?
Given fractions are 585/414,346/720
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 585/414,346/720, numerators are 585,346
Denominators are 414,720
The GCF of 585,346 is 1 .
LCM of 414,720 is 16560.
The greatest common factor of 585/414,346/720 = [GCF of 585,346]/[LCM of 414,720]= 1/16560
Therefore, the GCF of 585/414,346/720 is 1/16560.
To find the highest common factor of 585,346, we have to find the factors of both numbers and list the highest common factor.
The factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585
The factors of 346 are 1, 2, 173, 346
The HCF of 585,346 is 1.
Lets's calculate GCF of 585,346
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 585,346 By Matching Biggest Common Factor Method
Now, list down the factors of 585
:1,3,5,9,13,15,39,45,65,117,195,585
Now, list down the factors of 346
:1,2,173,346
Greatest Common Factor
We found the factors 585,346 . The biggest common factor number is the GCF number.
So the greatest common factor 585,346 is 1.
Lets's calculate LCM of 414,720
| 2 | 414, 720 |
| 3 | 207, 360 |
| 3 | 69, 120 |
| 23, 40 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 23 x 40 = 16560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/16560
Therefore, the GCF of Fractions 585/414,346/720 is 1/16560
Least Common Multiple of 414,720 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 414,720 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,720) = 18
common factors(in case of two or more numbers have common factors) = 1
GCF(414,720) x common factors =18 x 1 = 18
LCM(414,720) = ( 414 × 720 ) / 18
LCM(414,720) = 298080 / 18
LCM(414,720) = 16560
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FAQs on GCF of Fractions of 585/414, 346/720
1. What is the HCF of 585,346?
The HCF of 585,346 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 585/414, 346/720?
Answer: GCF of Numerators as per given numbers 585/414, 346/720 is
GCF of Numerators i.e. for 585,346 is 1
LCM of denominators i.e. for 414,720 is 16560.
Thus, GCF of Fractions is 1/16560.Finally, GCF of Fractions for 585/414, 346/720 is 1/16560.