GCF of 3171/689, 5100/2816
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3171/689, 5100/2816 i.e 3/1940224 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3171/689, 5100/2816.
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 3171/689,5100/2816?
Given fractions are 3171/689,5100/2816
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 3171/689,5100/2816, numerators are 3171,5100
Denominators are 689,2816
The GCF of 3171,5100 is 3 .
LCM of 689,2816 is 1940224.
The greatest common factor of 3171/689,5100/2816 = [GCF of 3171,5100]/[LCM of 689,2816]= 3/1940224
Therefore, the GCF of 3171/689,5100/2816 is 3/1940224.
To find the highest common factor of 3171,5100, we have to find the factors of both numbers and list the highest common factor.
The factors of 3171 are 1, 3, 7, 21, 151, 453, 1057, 3171
The factors of 5100 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 25, 30, 34, 50, 51, 60, 68, 75, 85, 100, 102, 150, 170, 204, 255, 300, 340, 425, 510, 850, 1020, 1275, 1700, 2550, 5100
The HCF of 3171,5100 is 3.
Lets's calculate GCF of 3171,5100
| 3 | 3171, 5100 |
| 1057, 1700 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 3171,5100 By Matching Biggest Common Factor Method
Now, list down the factors of 3171
:1,3,7,21,151,453,1057,3171
Now, list down the factors of 5100
:1,2,3,4,5,6,10,12,15,17,20,25,30,34,50,51,60,68,75,85,100,102,150,170,204,255,300,340,425,510,850,1020,1275,1700,2550,5100
Greatest Common Factor
We found the factors 3171,5100 . The biggest common factor number is the GCF number.
So the greatest common factor 3171,5100 is 3.
Lets's calculate LCM of 689,2816
Given numbers has no common factors except 1. So, there LCM is their product i.e 1940224
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1940224
Therefore, the GCF of Fractions 3171/689,5100/2816 is 3/1940224
Least Common Multiple of 689,2816 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 689,2816 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(689,2816) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(689,2816) x common factors =1 x 1 = 1
LCM(689,2816) = ( 689 × 2816 ) / 1
LCM(689,2816) = 1940224 / 1
LCM(689,2816) = 1940224
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FAQs on GCF of Fractions of 3171/689, 5100/2816
1. What is the HCF of 3171,5100?
The HCF of 3171,5100 is 3
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 3171/689, 5100/2816?
Answer: GCF of Numerators as per given numbers 3171/689, 5100/2816 is
GCF of Numerators i.e. for 3171,5100 is 3
LCM of denominators i.e. for 689,2816 is 1940224.
Thus, GCF of Fractions is 3/1940224.Finally, GCF of Fractions for 3171/689, 5100/2816 is 3/1940224.