GCF of 814/84, 138/18, 817/23
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 814/84, 138/18, 817/23 i.e 1/5796 easily. The following is the detailed procedure to determine the greatest common factor of fractions 814/84, 138/18, 817/23.
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 814/84,138/18,817/23?
Given fractions are 814/84,138/18,817/23
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 814/84,138/18,817/23, numerators are 814,138,817
Denominators are 84,18,23
The GCF of 814,138,817 is 1 .
LCM of 84,18,23 is 5796.
The greatest common factor of 814/84,138/18,817/23 = [GCF of 814,138,817]/[LCM of 84,18,23]= 1/5796
Therefore, the GCF of 814/84,138/18,817/23 is 1/5796.
To find the highest common factor of 814,138,817, we have to find the factors of both numbers and list the highest common factor.
The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814
The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138
The factors of 817 are 1, 19, 43, 817
The HCF of 814,138,817 is 1.
Lets's calculate GCF of 814,138,817
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 814,138,817 By Matching Biggest Common Factor Method
Now, list down the factors of 814
:1,2,11,22,37,74,407,814
Now, list down the factors of 138
:1,2,3,6,23,46,69,138
Now, list down the factors of 817
:1,19,43,817
Greatest Common Factor
We found the factors 814,138,817 . The biggest common factor number is the GCF number.
So the greatest common factor 814,138,817 is 1.
Lets's calculate LCM of 84,18,23
| 2 | 84, 18, 23 |
| 3 | 42, 9, 23 |
| 14, 3, 23 |
∴ So the LCM of the given numbers is 2 x 3 x 14 x 3 x 23 = 5796
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5796
Therefore, the GCF of Fractions 814/84,138/18,817/23 is 1/5796
Least Common Multiple of 84,18,23 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 84,18,23 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,18,23) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(84,18,23) x common factors =1 x 6 = 6
LCM(84,18,23) = ( 84 × 18 × 23 ) / 6
LCM(84,18,23) = 34776 / 6
LCM(84,18,23) = 5796
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FAQs on GCF of Fractions of 814/84, 138/18, 817/23
1. What is the HCF of 814,138,817?
The HCF of 814,138,817 is 1
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 814/84, 138/18, 817/23?
Answer: GCF of Numerators as per given numbers 814/84, 138/18, 817/23 is
GCF of Numerators i.e. for 814,138,817 is 1
LCM of denominators i.e. for 84,18,23 is 5796.
Thus, GCF of Fractions is 1/5796.Finally, GCF of Fractions for 814/84, 138/18, 817/23 is 1/5796.