GCF of 87/188, 69/313, 216/200
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 87/188, 69/313, 216/200 i.e 3/2942200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 87/188, 69/313, 216/200.
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 87/188,69/313,216/200?
Given fractions are 87/188,69/313,216/200
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 87/188,69/313,216/200, numerators are 87,69,216
Denominators are 188,313,200
The GCF of 87,69,216 is 3 .
LCM of 188,313,200 is 2942200.
The greatest common factor of 87/188,69/313,216/200 = [GCF of 87,69,216]/[LCM of 188,313,200]= 3/2942200
Therefore, the GCF of 87/188,69/313,216/200 is 3/2942200.
To find the highest common factor of 87,69,216, we have to find the factors of both numbers and list the highest common factor.
The factors of 87 are 1, 3, 29, 87
The factors of 69 are 1, 3, 23, 69
The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
The HCF of 87,69,216 is 3.
Lets's calculate GCF of 87,69,216
| 3 | 87, 69, 216 |
| 29, 23, 72 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 87,69,216 By Matching Biggest Common Factor Method
Now, list down the factors of 87
:1,3,29,87
Now, list down the factors of 69
:1,3,23,69
Now, list down the factors of 216
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216
Greatest Common Factor
We found the factors 87,69,216 . The biggest common factor number is the GCF number.
So the greatest common factor 87,69,216 is 3.
Lets's calculate LCM of 188,313,200
| 2 | 188, 313, 200 |
| 2 | 94, 313, 100 |
| 47, 313, 50 |
∴ So the LCM of the given numbers is 2 x 2 x 47 x 313 x 50 = 2942200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/2942200
Therefore, the GCF of Fractions 87/188,69/313,216/200 is 3/2942200
Least Common Multiple of 188,313,200 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 188,313,200 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(188,313,200) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(188,313,200) x common factors =1 x 4 = 4
LCM(188,313,200) = ( 188 × 313 × 200 ) / 4
LCM(188,313,200) = 11768800 / 4
LCM(188,313,200) = 2942200
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FAQs on GCF of Fractions of 87/188, 69/313, 216/200
1. What is the HCF of 87,69,216?
The HCF of 87,69,216 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 87/188, 69/313, 216/200?
Answer: GCF of Numerators as per given numbers 87/188, 69/313, 216/200 is
GCF of Numerators i.e. for 87,69,216 is 3
LCM of denominators i.e. for 188,313,200 is 2942200.
Thus, GCF of Fractions is 3/2942200.Finally, GCF of Fractions for 87/188, 69/313, 216/200 is 3/2942200.