GCF of 578/296, 663/333, 510/162
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 578/296, 663/333, 510/162 i.e 17/23976 easily. The following is the detailed procedure to determine the greatest common factor of fractions 578/296, 663/333, 510/162.
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 578/296,663/333,510/162?
Given fractions are 578/296,663/333,510/162
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 578/296,663/333,510/162, numerators are 578,663,510
Denominators are 296,333,162
The GCF of 578,663,510 is 17 .
LCM of 296,333,162 is 23976.
The greatest common factor of 578/296,663/333,510/162 = [GCF of 578,663,510]/[LCM of 296,333,162]= 17/23976
Therefore, the GCF of 578/296,663/333,510/162 is 17/23976.
To find the highest common factor of 578,663,510, we have to find the factors of both numbers and list the highest common factor.
The factors of 578 are 1, 2, 17, 34, 289, 578
The factors of 663 are 1, 3, 13, 17, 39, 51, 221, 663
The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
The HCF of 578,663,510 is 17.
Lets's calculate GCF of 578,663,510
| 17 | 578, 663, 510 |
| 34, 39, 30 |
∴ So the GCF of the given numbers is 17 = 17
Greatest Common Factor of 578,663,510 By Matching Biggest Common Factor Method
Now, list down the factors of 578
:1,2,17,34,289,578
Now, list down the factors of 663
:1,3,13,17,39,51,221,663
Now, list down the factors of 510
:1,2,3,5,6,10,15,17,30,34,51,85,102,170,255,510
Greatest Common Factor
We found the factors 578,663,510 . The biggest common factor number is the GCF number.
So the greatest common factor 578,663,510 is 17.
Lets's calculate LCM of 296,333,162
| 2 | 296, 333, 162 |
| 3 | 148, 333, 81 |
| 3 | 148, 111, 27 |
| 37 | 148, 37, 9 |
| 4, 1, 9 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 37 x 4 x 1 x 9 = 23976
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/23976
Therefore, the GCF of Fractions 578/296,663/333,510/162 is 17/23976
Least Common Multiple of 296,333,162 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 296,333,162 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(296,333,162) = 1
common factors(in case of two or more numbers have common factors) = 666
GCF(296,333,162) x common factors =1 x 666 = 666
LCM(296,333,162) = ( 296 × 333 × 162 ) / 666
LCM(296,333,162) = 15968016 / 666
LCM(296,333,162) = 23976
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FAQs on GCF of Fractions of 578/296, 663/333, 510/162
1. What is the HCF of 578,663,510?
The HCF of 578,663,510 is 17
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 578/296, 663/333, 510/162?
Answer: GCF of Numerators as per given numbers 578/296, 663/333, 510/162 is
GCF of Numerators i.e. for 578,663,510 is 17
LCM of denominators i.e. for 296,333,162 is 23976.
Thus, GCF of Fractions is 17/23976.Finally, GCF of Fractions for 578/296, 663/333, 510/162 is 17/23976.