GCF of 638/259, 522/706
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 638/259, 522/706 i.e 58/182854 easily. The following is the detailed procedure to determine the greatest common factor of fractions 638/259, 522/706.
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 638/259,522/706?
Given fractions are 638/259,522/706
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 638/259,522/706, numerators are 638,522
Denominators are 259,706
The GCF of 638,522 is 58 .
LCM of 259,706 is 182854.
The greatest common factor of 638/259,522/706 = [GCF of 638,522]/[LCM of 259,706]= 58/182854
Therefore, the GCF of 638/259,522/706 is 58/182854.
To find the highest common factor of 638,522, we have to find the factors of both numbers and list the highest common factor.
The factors of 638 are 1, 2, 11, 22, 29, 58, 319, 638
The factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522
The HCF of 638,522 is 58.
Lets's calculate GCF of 638,522
| 2 | 638, 522 |
| 29 | 319, 261 |
| 11, 9 |
∴ So the GCF of the given numbers is 2 x 29 = 58
Greatest Common Factor of 638,522 By Matching Biggest Common Factor Method
Now, list down the factors of 638
:1,2,11,22,29,58,319,638
Now, list down the factors of 522
:1,2,3,6,9,18,29,58,87,174,261,522
Greatest Common Factor
We found the factors 638,522 . The biggest common factor number is the GCF number.
So the greatest common factor 638,522 is 58.
Lets's calculate LCM of 259,706
Given numbers has no common factors except 1. So, there LCM is their product i.e 182854
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 58/182854
Therefore, the GCF of Fractions 638/259,522/706 is 58/182854
Least Common Multiple of 259,706 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 259,706 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(259,706) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(259,706) x common factors =1 x 1 = 1
LCM(259,706) = ( 259 × 706 ) / 1
LCM(259,706) = 182854 / 1
LCM(259,706) = 182854
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FAQs on GCF of Fractions of 638/259, 522/706
1. What is the HCF of 638,522?
The HCF of 638,522 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 638/259, 522/706?
Answer: GCF of Numerators as per given numbers 638/259, 522/706 is
GCF of Numerators i.e. for 638,522 is 58
LCM of denominators i.e. for 259,706 is 182854.
Thus, GCF of Fractions is 58/182854.Finally, GCF of Fractions for 638/259, 522/706 is 58/182854.