GCF of 80/21, 161/35, 105/107
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 80/21, 161/35, 105/107 i.e 1/11235 easily. The following is the detailed procedure to determine the greatest common factor of fractions 80/21, 161/35, 105/107.
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 80/21,161/35,105/107?
Given fractions are 80/21,161/35,105/107
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 80/21,161/35,105/107, numerators are 80,161,105
Denominators are 21,35,107
The GCF of 80,161,105 is 1 .
LCM of 21,35,107 is 11235.
The greatest common factor of 80/21,161/35,105/107 = [GCF of 80,161,105]/[LCM of 21,35,107]= 1/11235
Therefore, the GCF of 80/21,161/35,105/107 is 1/11235.
To find the highest common factor of 80,161,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The factors of 161 are 1, 7, 23, 161
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 80,161,105 is 1.
Lets's calculate GCF of 80,161,105
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 80,161,105 By Matching Biggest Common Factor Method
Now, list down the factors of 80
:1,2,4,5,8,10,16,20,40,80
Now, list down the factors of 161
:1,7,23,161
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 80,161,105 . The biggest common factor number is the GCF number.
So the greatest common factor 80,161,105 is 1.
Lets's calculate LCM of 21,35,107
| 7 | 21, 35, 107 |
| 3, 5, 107 |
∴ So the LCM of the given numbers is 7 x 3 x 5 x 107 = 11235
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11235
Therefore, the GCF of Fractions 80/21,161/35,105/107 is 1/11235
Least Common Multiple of 21,35,107 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 21,35,107 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,35,107) = 1
common factors(in case of two or more numbers have common factors) = 7
GCF(21,35,107) x common factors =1 x 7 = 7
LCM(21,35,107) = ( 21 × 35 × 107 ) / 7
LCM(21,35,107) = 78645 / 7
LCM(21,35,107) = 11235
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FAQs on GCF of Fractions of 80/21, 161/35, 105/107
1. What is the HCF of 80,161,105?
The HCF of 80,161,105 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 80/21, 161/35, 105/107?
Answer: GCF of Numerators as per given numbers 80/21, 161/35, 105/107 is
GCF of Numerators i.e. for 80,161,105 is 1
LCM of denominators i.e. for 21,35,107 is 11235.
Thus, GCF of Fractions is 1/11235.Finally, GCF of Fractions for 80/21, 161/35, 105/107 is 1/11235.