GCF of 216/645, 1600/713
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 216/645, 1600/713 i.e 8/459885 easily. The following is the detailed procedure to determine the greatest common factor of fractions 216/645, 1600/713.
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 216/645,1600/713?
Given fractions are 216/645,1600/713
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 216/645,1600/713, numerators are 216,1600
Denominators are 645,713
The GCF of 216,1600 is 8 .
LCM of 645,713 is 459885.
The greatest common factor of 216/645,1600/713 = [GCF of 216,1600]/[LCM of 645,713]= 8/459885
Therefore, the GCF of 216/645,1600/713 is 8/459885.
To find the highest common factor of 216,1600, we have to find the factors of both numbers and list the highest common factor.
The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
The factors of 1600 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600
The HCF of 216,1600 is 8.
Lets's calculate GCF of 216,1600
| 2 | 216, 1600 |
| 2 | 108, 800 |
| 2 | 54, 400 |
| 27, 200 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 216,1600 By Matching Biggest Common Factor Method
Now, list down the factors of 216
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216
Now, list down the factors of 1600
:1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,160,200,320,400,800,1600
Greatest Common Factor
We found the factors 216,1600 . The biggest common factor number is the GCF number.
So the greatest common factor 216,1600 is 8.
Lets's calculate LCM of 645,713
Given numbers has no common factors except 1. So, there LCM is their product i.e 459885
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/459885
Therefore, the GCF of Fractions 216/645,1600/713 is 8/459885
Least Common Multiple of 645,713 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 645,713 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(645,713) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(645,713) x common factors =1 x 1 = 1
LCM(645,713) = ( 645 × 713 ) / 1
LCM(645,713) = 459885 / 1
LCM(645,713) = 459885
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FAQs on GCF of Fractions of 216/645, 1600/713
1. What is the HCF of 216,1600?
The HCF of 216,1600 is 8
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 216/645, 1600/713?
Answer: GCF of Numerators as per given numbers 216/645, 1600/713 is
GCF of Numerators i.e. for 216,1600 is 8
LCM of denominators i.e. for 645,713 is 459885.
Thus, GCF of Fractions is 8/459885.Finally, GCF of Fractions for 216/645, 1600/713 is 8/459885.