GCF of 586/30, 686/315
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 586/30, 686/315 i.e 2/630 easily. The following is the detailed procedure to determine the greatest common factor of fractions 586/30, 686/315.
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 586/30,686/315?
Given fractions are 586/30,686/315
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 586/30,686/315, numerators are 586,686
Denominators are 30,315
The GCF of 586,686 is 2 .
LCM of 30,315 is 630.
The greatest common factor of 586/30,686/315 = [GCF of 586,686]/[LCM of 30,315]= 2/630
Therefore, the GCF of 586/30,686/315 is 2/630.
To find the highest common factor of 586,686, we have to find the factors of both numbers and list the highest common factor.
The factors of 586 are 1, 2, 293, 586
The factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686
The HCF of 586,686 is 2.
Lets's calculate GCF of 586,686
| 2 | 586, 686 |
| 293, 343 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 586,686 By Matching Biggest Common Factor Method
Now, list down the factors of 586
:1,2,293,586
Now, list down the factors of 686
:1,2,7,14,49,98,343,686
Greatest Common Factor
We found the factors 586,686 . The biggest common factor number is the GCF number.
So the greatest common factor 586,686 is 2.
Lets's calculate LCM of 30,315
| 3 | 30, 315 |
| 5 | 10, 105 |
| 2, 21 |
∴ So the LCM of the given numbers is 3 x 5 x 2 x 21 = 630
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/630
Therefore, the GCF of Fractions 586/30,686/315 is 2/630
Least Common Multiple of 30,315 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 30,315 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,315) = 15
common factors(in case of two or more numbers have common factors) = 1
GCF(30,315) x common factors =15 x 1 = 15
LCM(30,315) = ( 30 × 315 ) / 15
LCM(30,315) = 9450 / 15
LCM(30,315) = 630
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FAQs on GCF of Fractions of 586/30, 686/315
1. What is the HCF of 586,686?
The HCF of 586,686 is 2
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 586/30, 686/315?
Answer: GCF of Numerators as per given numbers 586/30, 686/315 is
GCF of Numerators i.e. for 586,686 is 2
LCM of denominators i.e. for 30,315 is 630.
Thus, GCF of Fractions is 2/630.Finally, GCF of Fractions for 586/30, 686/315 is 2/630.