GCF of 82/17, 128/54, 472/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 82/17, 128/54, 472/419 i.e 2/384642 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/17, 128/54, 472/419.
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 82/17,128/54,472/419?
Given fractions are 82/17,128/54,472/419
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 82/17,128/54,472/419, numerators are 82,128,472
Denominators are 17,54,419
The GCF of 82,128,472 is 2 .
LCM of 17,54,419 is 384642.
The greatest common factor of 82/17,128/54,472/419 = [GCF of 82,128,472]/[LCM of 17,54,419]= 2/384642
Therefore, the GCF of 82/17,128/54,472/419 is 2/384642.
To find the highest common factor of 82,128,472, we have to find the factors of both numbers and list the highest common factor.
The factors of 82 are 1, 2, 41, 82
The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128
The factors of 472 are 1, 2, 4, 8, 59, 118, 236, 472
The HCF of 82,128,472 is 2.
Lets's calculate GCF of 82,128,472
| 2 | 82, 128, 472 |
| 41, 64, 236 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 82,128,472 By Matching Biggest Common Factor Method
Now, list down the factors of 82
:1,2,41,82
Now, list down the factors of 128
:1,2,4,8,16,32,64,128
Now, list down the factors of 472
:1,2,4,8,59,118,236,472
Greatest Common Factor
We found the factors 82,128,472 . The biggest common factor number is the GCF number.
So the greatest common factor 82,128,472 is 2.
Lets's calculate LCM of 17,54,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 384642
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/384642
Therefore, the GCF of Fractions 82/17,128/54,472/419 is 2/384642
Least Common Multiple of 17,54,419 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 17,54,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(17,54,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(17,54,419) x common factors =1 x 1 = 1
LCM(17,54,419) = ( 17 × 54 × 419 ) / 1
LCM(17,54,419) = 384642 / 1
LCM(17,54,419) = 384642
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FAQs on GCF of Fractions of 82/17, 128/54, 472/419
1. What is the HCF of 82,128,472?
The HCF of 82,128,472 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 82/17, 128/54, 472/419?
Answer: GCF of Numerators as per given numbers 82/17, 128/54, 472/419 is
GCF of Numerators i.e. for 82,128,472 is 2
LCM of denominators i.e. for 17,54,419 is 384642.
Thus, GCF of Fractions is 2/384642.Finally, GCF of Fractions for 82/17, 128/54, 472/419 is 2/384642.