GCF of 306/582, 612/142
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 306/582, 612/142 i.e 306/41322 easily. The following is the detailed procedure to determine the greatest common factor of fractions 306/582, 612/142.
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 306/582,612/142?
Given fractions are 306/582,612/142
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 306/582,612/142, numerators are 306,612
Denominators are 582,142
The GCF of 306,612 is 306 .
LCM of 582,142 is 41322.
The greatest common factor of 306/582,612/142 = [GCF of 306,612]/[LCM of 582,142]= 306/41322
Therefore, the GCF of 306/582,612/142 is 306/41322.
To find the highest common factor of 306,612, we have to find the factors of both numbers and list the highest common factor.
The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
The factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612
The HCF of 306,612 is 306.
Lets's calculate GCF of 306,612
| 2 | 306, 612 |
| 3 | 153, 306 |
| 3 | 51, 102 |
| 17 | 17, 34 |
| 1, 2 |
∴ So the GCF of the given numbers is 2 x 3 x 3 x 17 = 306
Greatest Common Factor of 306,612 By Matching Biggest Common Factor Method
Now, list down the factors of 306
:1,2,3,6,9,17,18,34,51,102,153,306
Now, list down the factors of 612
:1,2,3,4,6,9,12,17,18,34,36,51,68,102,153,204,306,612
Greatest Common Factor
We found the factors 306,612 . The biggest common factor number is the GCF number.
So the greatest common factor 306,612 is 306.
Lets's calculate LCM of 582,142
| 2 | 582, 142 |
| 291, 71 |
∴ So the LCM of the given numbers is 2 x 291 x 71 = 41322
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 306/41322
Therefore, the GCF of Fractions 306/582,612/142 is 306/41322
Least Common Multiple of 582,142 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 582,142 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(582,142) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(582,142) x common factors =2 x 1 = 2
LCM(582,142) = ( 582 × 142 ) / 2
LCM(582,142) = 82644 / 2
LCM(582,142) = 41322
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FAQs on GCF of Fractions of 306/582, 612/142
1. What is the HCF of 306,612?
The HCF of 306,612 is 306
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 306/582, 612/142?
Answer: GCF of Numerators as per given numbers 306/582, 612/142 is
GCF of Numerators i.e. for 306,612 is 306
LCM of denominators i.e. for 582,142 is 41322.
Thus, GCF of Fractions is 306/41322.Finally, GCF of Fractions for 306/582, 612/142 is 306/41322.