GCF of 128/409, 162/382
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 128/409, 162/382 i.e 2/156238 easily. The following is the detailed procedure to determine the greatest common factor of fractions 128/409, 162/382.
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 128/409,162/382?
Given fractions are 128/409,162/382
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 128/409,162/382, numerators are 128,162
Denominators are 409,382
The GCF of 128,162 is 2 .
LCM of 409,382 is 156238.
The greatest common factor of 128/409,162/382 = [GCF of 128,162]/[LCM of 409,382]= 2/156238
Therefore, the GCF of 128/409,162/382 is 2/156238.
To find the highest common factor of 128,162, we have to find the factors of both numbers and list the highest common factor.
The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128
The factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162
The HCF of 128,162 is 2.
Lets's calculate GCF of 128,162
| 2 | 128, 162 |
| 64, 81 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 128,162 By Matching Biggest Common Factor Method
Now, list down the factors of 128
:1,2,4,8,16,32,64,128
Now, list down the factors of 162
:1,2,3,6,9,18,27,54,81,162
Greatest Common Factor
We found the factors 128,162 . The biggest common factor number is the GCF number.
So the greatest common factor 128,162 is 2.
Lets's calculate LCM of 409,382
Given numbers has no common factors except 1. So, there LCM is their product i.e 156238
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/156238
Therefore, the GCF of Fractions 128/409,162/382 is 2/156238
Least Common Multiple of 409,382 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 409,382 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(409,382) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(409,382) x common factors =1 x 1 = 1
LCM(409,382) = ( 409 × 382 ) / 1
LCM(409,382) = 156238 / 1
LCM(409,382) = 156238
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FAQs on GCF of Fractions of 128/409, 162/382
1. What is the HCF of 128,162?
The HCF of 128,162 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 128/409, 162/382?
Answer: GCF of Numerators as per given numbers 128/409, 162/382 is
GCF of Numerators i.e. for 128,162 is 2
LCM of denominators i.e. for 409,382 is 156238.
Thus, GCF of Fractions is 2/156238.Finally, GCF of Fractions for 128/409, 162/382 is 2/156238.