GCF of 522/76, 638/582
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 522/76, 638/582 i.e 58/22116 easily. The following is the detailed procedure to determine the greatest common factor of fractions 522/76, 638/582.
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 522/76,638/582?
Given fractions are 522/76,638/582
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 522/76,638/582, numerators are 522,638
Denominators are 76,582
The GCF of 522,638 is 58 .
LCM of 76,582 is 22116.
The greatest common factor of 522/76,638/582 = [GCF of 522,638]/[LCM of 76,582]= 58/22116
Therefore, the GCF of 522/76,638/582 is 58/22116.
To find the highest common factor of 522,638, we have to find the factors of both numbers and list the highest common factor.
The factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522
The factors of 638 are 1, 2, 11, 22, 29, 58, 319, 638
The HCF of 522,638 is 58.
Lets's calculate GCF of 522,638
| 2 | 522, 638 |
| 29 | 261, 319 |
| 9, 11 |
∴ So the GCF of the given numbers is 2 x 29 = 58
Greatest Common Factor of 522,638 By Matching Biggest Common Factor Method
Now, list down the factors of 522
:1,2,3,6,9,18,29,58,87,174,261,522
Now, list down the factors of 638
:1,2,11,22,29,58,319,638
Greatest Common Factor
We found the factors 522,638 . The biggest common factor number is the GCF number.
So the greatest common factor 522,638 is 58.
Lets's calculate LCM of 76,582
| 2 | 76, 582 |
| 38, 291 |
∴ So the LCM of the given numbers is 2 x 38 x 291 = 22116
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 58/22116
Therefore, the GCF of Fractions 522/76,638/582 is 58/22116
Least Common Multiple of 76,582 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 76,582 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,582) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(76,582) x common factors =2 x 1 = 2
LCM(76,582) = ( 76 × 582 ) / 2
LCM(76,582) = 44232 / 2
LCM(76,582) = 22116
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FAQs on GCF of Fractions of 522/76, 638/582
1. What is the HCF of 522,638?
The HCF of 522,638 is 58
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 522/76, 638/582?
Answer: GCF of Numerators as per given numbers 522/76, 638/582 is
GCF of Numerators i.e. for 522,638 is 58
LCM of denominators i.e. for 76,582 is 22116.
Thus, GCF of Fractions is 58/22116.Finally, GCF of Fractions for 522/76, 638/582 is 58/22116.