GCF of 9765/70, 3000/557
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9765/70, 3000/557 i.e 15/38990 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9765/70, 3000/557.
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 9765/70,3000/557?
Given fractions are 9765/70,3000/557
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 9765/70,3000/557, numerators are 9765,3000
Denominators are 70,557
The GCF of 9765,3000 is 15 .
LCM of 70,557 is 38990.
The greatest common factor of 9765/70,3000/557 = [GCF of 9765,3000]/[LCM of 70,557]= 15/38990
Therefore, the GCF of 9765/70,3000/557 is 15/38990.
To find the highest common factor of 9765,3000, we have to find the factors of both numbers and list the highest common factor.
The factors of 9765 are 1, 3, 5, 7, 9, 15, 21, 31, 35, 45, 63, 93, 105, 155, 217, 279, 315, 465, 651, 1085, 1395, 1953, 3255, 9765
The factors of 3000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 125, 150, 200, 250, 300, 375, 500, 600, 750, 1000, 1500, 3000
The HCF of 9765,3000 is 15.
Lets's calculate GCF of 9765,3000
| 3 | 9765, 3000 |
| 5 | 3255, 1000 |
| 651, 200 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 9765,3000 By Matching Biggest Common Factor Method
Now, list down the factors of 9765
:1,3,5,7,9,15,21,31,35,45,63,93,105,155,217,279,315,465,651,1085,1395,1953,3255,9765
Now, list down the factors of 3000
:1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,125,150,200,250,300,375,500,600,750,1000,1500,3000
Greatest Common Factor
We found the factors 9765,3000 . The biggest common factor number is the GCF number.
So the greatest common factor 9765,3000 is 15.
Lets's calculate LCM of 70,557
Given numbers has no common factors except 1. So, there LCM is their product i.e 38990
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/38990
Therefore, the GCF of Fractions 9765/70,3000/557 is 15/38990
Least Common Multiple of 70,557 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 70,557 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,557) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(70,557) x common factors =1 x 1 = 1
LCM(70,557) = ( 70 × 557 ) / 1
LCM(70,557) = 38990 / 1
LCM(70,557) = 38990
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FAQs on GCF of Fractions of 9765/70, 3000/557
1. What is the HCF of 9765,3000?
The HCF of 9765,3000 is 15
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 9765/70, 3000/557?
Answer: GCF of Numerators as per given numbers 9765/70, 3000/557 is
GCF of Numerators i.e. for 9765,3000 is 15
LCM of denominators i.e. for 70,557 is 38990.
Thus, GCF of Fractions is 15/38990.Finally, GCF of Fractions for 9765/70, 3000/557 is 15/38990.