GCF of 6975/780, 5200/724
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6975/780, 5200/724 i.e 25/141180 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6975/780, 5200/724.
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 6975/780,5200/724?
Given fractions are 6975/780,5200/724
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 6975/780,5200/724, numerators are 6975,5200
Denominators are 780,724
The GCF of 6975,5200 is 25 .
LCM of 780,724 is 141180.
The greatest common factor of 6975/780,5200/724 = [GCF of 6975,5200]/[LCM of 780,724]= 25/141180
Therefore, the GCF of 6975/780,5200/724 is 25/141180.
To find the highest common factor of 6975,5200, we have to find the factors of both numbers and list the highest common factor.
The factors of 6975 are 1, 3, 5, 9, 15, 25, 31, 45, 75, 93, 155, 225, 279, 465, 775, 1395, 2325, 6975
The factors of 5200 are 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 40, 50, 52, 65, 80, 100, 104, 130, 200, 208, 260, 325, 400, 520, 650, 1040, 1300, 2600, 5200
The HCF of 6975,5200 is 25.
Lets's calculate GCF of 6975,5200
| 5 | 6975, 5200 |
| 5 | 1395, 1040 |
| 279, 208 |
∴ So the GCF of the given numbers is 5 x 5 = 25
Greatest Common Factor of 6975,5200 By Matching Biggest Common Factor Method
Now, list down the factors of 6975
:1,3,5,9,15,25,31,45,75,93,155,225,279,465,775,1395,2325,6975
Now, list down the factors of 5200
:1,2,4,5,8,10,13,16,20,25,26,40,50,52,65,80,100,104,130,200,208,260,325,400,520,650,1040,1300,2600,5200
Greatest Common Factor
We found the factors 6975,5200 . The biggest common factor number is the GCF number.
So the greatest common factor 6975,5200 is 25.
Lets's calculate LCM of 780,724
| 2 | 780, 724 |
| 2 | 390, 362 |
| 195, 181 |
∴ So the LCM of the given numbers is 2 x 2 x 195 x 181 = 141180
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 25/141180
Therefore, the GCF of Fractions 6975/780,5200/724 is 25/141180
Least Common Multiple of 780,724 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 780,724 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(780,724) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(780,724) x common factors =4 x 1 = 4
LCM(780,724) = ( 780 × 724 ) / 4
LCM(780,724) = 564720 / 4
LCM(780,724) = 141180
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FAQs on GCF of Fractions of 6975/780, 5200/724
1. What is the HCF of 6975,5200?
The HCF of 6975,5200 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 6975/780, 5200/724?
Answer: GCF of Numerators as per given numbers 6975/780, 5200/724 is
GCF of Numerators i.e. for 6975,5200 is 25
LCM of denominators i.e. for 780,724 is 141180.
Thus, GCF of Fractions is 25/141180.Finally, GCF of Fractions for 6975/780, 5200/724 is 25/141180.