GCF of 523/404, 120/707
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 523/404, 120/707 i.e 1/2828 easily. The following is the detailed procedure to determine the greatest common factor of fractions 523/404, 120/707.
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 523/404,120/707?
Given fractions are 523/404,120/707
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 523/404,120/707, numerators are 523,120
Denominators are 404,707
The GCF of 523,120 is 1 .
LCM of 404,707 is 2828.
The greatest common factor of 523/404,120/707 = [GCF of 523,120]/[LCM of 404,707]= 1/2828
Therefore, the GCF of 523/404,120/707 is 1/2828.
To find the highest common factor of 523,120, 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 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 523,120 is 1.
Lets's calculate GCF of 523,120
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 523,120 By Matching Biggest Common Factor Method
Now, list down the factors of 523
:1,523
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Greatest Common Factor
We found the factors 523,120 . The biggest common factor number is the GCF number.
So the greatest common factor 523,120 is 1.
Lets's calculate LCM of 404,707
| 101 | 404, 707 |
| 4, 7 |
∴ So the LCM of the given numbers is 101 x 4 x 7 = 2828
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2828
Therefore, the GCF of Fractions 523/404,120/707 is 1/2828
Least Common Multiple of 404,707 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 404,707 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(404,707) = 101
common factors(in case of two or more numbers have common factors) = 1
GCF(404,707) x common factors =101 x 1 = 101
LCM(404,707) = ( 404 × 707 ) / 101
LCM(404,707) = 285628 / 101
LCM(404,707) = 2828
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FAQs on GCF of Fractions of 523/404, 120/707
1. What is the HCF of 523,120?
The HCF of 523,120 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 523/404, 120/707?
Answer: GCF of Numerators as per given numbers 523/404, 120/707 is
GCF of Numerators i.e. for 523,120 is 1
LCM of denominators i.e. for 404,707 is 2828.
Thus, GCF of Fractions is 1/2828.Finally, GCF of Fractions for 523/404, 120/707 is 1/2828.