GCF of 504/769, 120/745
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 504/769, 120/745 i.e 24/572905 easily. The following is the detailed procedure to determine the greatest common factor of fractions 504/769, 120/745.
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 504/769,120/745?
Given fractions are 504/769,120/745
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 504/769,120/745, numerators are 504,120
Denominators are 769,745
The GCF of 504,120 is 24 .
LCM of 769,745 is 572905.
The greatest common factor of 504/769,120/745 = [GCF of 504,120]/[LCM of 769,745]= 24/572905
Therefore, the GCF of 504/769,120/745 is 24/572905.
To find the highest common factor of 504,120, we have to find the factors of both numbers and list the highest common factor.
The factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 504,120 is 24.
Lets's calculate GCF of 504,120
| 2 | 504, 120 |
| 2 | 252, 60 |
| 2 | 126, 30 |
| 3 | 63, 15 |
| 21, 5 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
Greatest Common Factor of 504,120 By Matching Biggest Common Factor Method
Now, list down the factors of 504
:1,2,3,4,6,7,8,9,12,14,18,21,24,28,36,42,56,63,72,84,126,168,252,504
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 504,120 . The biggest common factor number is the GCF number.
So the greatest common factor 504,120 is 24.
Lets's calculate LCM of 769,745
Given numbers has no common factors except 1. So, there LCM is their product i.e 572905
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/572905
Therefore, the GCF of Fractions 504/769,120/745 is 24/572905
Least Common Multiple of 769,745 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 769,745 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(769,745) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(769,745) x common factors =1 x 1 = 1
LCM(769,745) = ( 769 × 745 ) / 1
LCM(769,745) = 572905 / 1
LCM(769,745) = 572905
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FAQs on GCF of Fractions of 504/769, 120/745
1. What is the HCF of 504,120?
The HCF of 504,120 is 24
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 504/769, 120/745?
Answer: GCF of Numerators as per given numbers 504/769, 120/745 is
GCF of Numerators i.e. for 504,120 is 24
LCM of denominators i.e. for 769,745 is 572905.
Thus, GCF of Fractions is 24/572905.Finally, GCF of Fractions for 504/769, 120/745 is 24/572905.