GCF of 386/409, 3200/9688
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 386/409, 3200/9688 i.e 2/3962392 easily. The following is the detailed procedure to determine the greatest common factor of fractions 386/409, 3200/9688.
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 386/409,3200/9688?
Given fractions are 386/409,3200/9688
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 386/409,3200/9688, numerators are 386,3200
Denominators are 409,9688
The GCF of 386,3200 is 2 .
LCM of 409,9688 is 3962392.
The greatest common factor of 386/409,3200/9688 = [GCF of 386,3200]/[LCM of 409,9688]= 2/3962392
Therefore, the GCF of 386/409,3200/9688 is 2/3962392.
To find the highest common factor of 386,3200, we have to find the factors of both numbers and list the highest common factor.
The factors of 386 are 1, 2, 193, 386
The factors of 3200 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 320, 400, 640, 800, 1600, 3200
The HCF of 386,3200 is 2.
Lets's calculate GCF of 386,3200
| 2 | 386, 3200 |
| 193, 1600 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 386,3200 By Matching Biggest Common Factor Method
Now, list down the factors of 386
:1,2,193,386
Now, list down the factors of 3200
:1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,128,160,200,320,400,640,800,1600,3200
Greatest Common Factor
We found the factors 386,3200 . The biggest common factor number is the GCF number.
So the greatest common factor 386,3200 is 2.
Lets's calculate LCM of 409,9688
Given numbers has no common factors except 1. So, there LCM is their product i.e 3962392
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3962392
Therefore, the GCF of Fractions 386/409,3200/9688 is 2/3962392
Least Common Multiple of 409,9688 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 409,9688 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(409,9688) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(409,9688) x common factors =1 x 1 = 1
LCM(409,9688) = ( 409 × 9688 ) / 1
LCM(409,9688) = 3962392 / 1
LCM(409,9688) = 3962392
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FAQs on GCF of Fractions of 386/409, 3200/9688
1. What is the HCF of 386,3200?
The HCF of 386,3200 is 2
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 386/409, 3200/9688?
Answer: GCF of Numerators as per given numbers 386/409, 3200/9688 is
GCF of Numerators i.e. for 386,3200 is 2
LCM of denominators i.e. for 409,9688 is 3962392.
Thus, GCF of Fractions is 2/3962392.Finally, GCF of Fractions for 386/409, 3200/9688 is 2/3962392.