GCF of 600/69, 725/114
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 600/69, 725/114 i.e 25/2622 easily. The following is the detailed procedure to determine the greatest common factor of fractions 600/69, 725/114.
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 600/69,725/114?
Given fractions are 600/69,725/114
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 600/69,725/114, numerators are 600,725
Denominators are 69,114
The GCF of 600,725 is 25 .
LCM of 69,114 is 2622.
The greatest common factor of 600/69,725/114 = [GCF of 600,725]/[LCM of 69,114]= 25/2622
Therefore, the GCF of 600/69,725/114 is 25/2622.
To find the highest common factor of 600,725, we have to find the factors of both numbers and list the highest common factor.
The factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
The factors of 725 are 1, 5, 25, 29, 145, 725
The HCF of 600,725 is 25.
Lets's calculate GCF of 600,725
| 5 | 600, 725 |
| 5 | 120, 145 |
| 24, 29 |
∴ So the GCF of the given numbers is 5 x 5 = 25
Greatest Common Factor of 600,725 By Matching Biggest Common Factor Method
Now, list down the factors of 600
:1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,150,200,300,600
Now, list down the factors of 725
:1,5,25,29,145,725
Greatest Common Factor
We found the factors 600,725 . The biggest common factor number is the GCF number.
So the greatest common factor 600,725 is 25.
Lets's calculate LCM of 69,114
| 3 | 69, 114 |
| 23, 38 |
∴ So the LCM of the given numbers is 3 x 23 x 38 = 2622
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 25/2622
Therefore, the GCF of Fractions 600/69,725/114 is 25/2622
Least Common Multiple of 69,114 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 69,114 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,114) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(69,114) x common factors =3 x 1 = 3
LCM(69,114) = ( 69 × 114 ) / 3
LCM(69,114) = 7866 / 3
LCM(69,114) = 2622
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FAQs on GCF of Fractions of 600/69, 725/114
1. What is the HCF of 600,725?
The HCF of 600,725 is 25
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 600/69, 725/114?
Answer: GCF of Numerators as per given numbers 600/69, 725/114 is
GCF of Numerators i.e. for 600,725 is 25
LCM of denominators i.e. for 69,114 is 2622.
Thus, GCF of Fractions is 25/2622.Finally, GCF of Fractions for 600/69, 725/114 is 25/2622.