GCF of 523/72, 338/675
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 523/72, 338/675 i.e 1/5400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 523/72, 338/675.
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 523/72,338/675?
Given fractions are 523/72,338/675
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 523/72,338/675, numerators are 523,338
Denominators are 72,675
The GCF of 523,338 is 1 .
LCM of 72,675 is 5400.
The greatest common factor of 523/72,338/675 = [GCF of 523,338]/[LCM of 72,675]= 1/5400
Therefore, the GCF of 523/72,338/675 is 1/5400.
To find the highest common factor of 523,338, we have to find the factors of both numbers and list the highest common factor.
The factors of 523 are 1, 523
The factors of 338 are 1, 2, 13, 26, 169, 338
The HCF of 523,338 is 1.
Lets's calculate GCF of 523,338
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 523,338 By Matching Biggest Common Factor Method
Now, list down the factors of 523
:1,523
Now, list down the factors of 338
:1,2,13,26,169,338
Greatest Common Factor
We found the factors 523,338 . The biggest common factor number is the GCF number.
So the greatest common factor 523,338 is 1.
Lets's calculate LCM of 72,675
| 3 | 72, 675 |
| 3 | 24, 225 |
| 8, 75 |
∴ So the LCM of the given numbers is 3 x 3 x 8 x 75 = 5400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5400
Therefore, the GCF of Fractions 523/72,338/675 is 1/5400
Least Common Multiple of 72,675 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 72,675 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(72,675) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(72,675) x common factors =9 x 1 = 9
LCM(72,675) = ( 72 × 675 ) / 9
LCM(72,675) = 48600 / 9
LCM(72,675) = 5400
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FAQs on GCF of Fractions of 523/72, 338/675
1. What is the HCF of 523,338?
The HCF of 523,338 is 1
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 523/72, 338/675?
Answer: GCF of Numerators as per given numbers 523/72, 338/675 is
GCF of Numerators i.e. for 523,338 is 1
LCM of denominators i.e. for 72,675 is 5400.
Thus, GCF of Fractions is 1/5400.Finally, GCF of Fractions for 523/72, 338/675 is 1/5400.