GCF of 506/578, 1023/1054
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 506/578, 1023/1054 i.e 11/17918 easily. The following is the detailed procedure to determine the greatest common factor of fractions 506/578, 1023/1054.
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 506/578,1023/1054?
Given fractions are 506/578,1023/1054
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 506/578,1023/1054, numerators are 506,1023
Denominators are 578,1054
The GCF of 506,1023 is 11 .
LCM of 578,1054 is 17918.
The greatest common factor of 506/578,1023/1054 = [GCF of 506,1023]/[LCM of 578,1054]= 11/17918
Therefore, the GCF of 506/578,1023/1054 is 11/17918.
To find the highest common factor of 506,1023, we have to find the factors of both numbers and list the highest common factor.
The factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506
The factors of 1023 are 1, 3, 11, 31, 33, 93, 341, 1023
The HCF of 506,1023 is 11.
Lets's calculate GCF of 506,1023
| 11 | 506, 1023 |
| 46, 93 |
∴ So the GCF of the given numbers is 11 = 11
Greatest Common Factor of 506,1023 By Matching Biggest Common Factor Method
Now, list down the factors of 506
:1,2,11,22,23,46,253,506
Now, list down the factors of 1023
:1,3,11,31,33,93,341,1023
Greatest Common Factor
We found the factors 506,1023 . The biggest common factor number is the GCF number.
So the greatest common factor 506,1023 is 11.
Lets's calculate LCM of 578,1054
| 2 | 578, 1054 |
| 17 | 289, 527 |
| 17, 31 |
∴ So the LCM of the given numbers is 2 x 17 x 17 x 31 = 17918
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/17918
Therefore, the GCF of Fractions 506/578,1023/1054 is 11/17918
Least Common Multiple of 578,1054 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 578,1054 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(578,1054) = 34
common factors(in case of two or more numbers have common factors) = 1
GCF(578,1054) x common factors =34 x 1 = 34
LCM(578,1054) = ( 578 × 1054 ) / 34
LCM(578,1054) = 609212 / 34
LCM(578,1054) = 17918
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FAQs on GCF of Fractions of 506/578, 1023/1054
1. What is the HCF of 506,1023?
The HCF of 506,1023 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 506/578, 1023/1054?
Answer: GCF of Numerators as per given numbers 506/578, 1023/1054 is
GCF of Numerators i.e. for 506,1023 is 11
LCM of denominators i.e. for 578,1054 is 17918.
Thus, GCF of Fractions is 11/17918.Finally, GCF of Fractions for 506/578, 1023/1054 is 11/17918.