GCF of 106/94, 406/217
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 106/94, 406/217 i.e 2/20398 easily. The following is the detailed procedure to determine the greatest common factor of fractions 106/94, 406/217.
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 106/94,406/217?
Given fractions are 106/94,406/217
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 106/94,406/217, numerators are 106,406
Denominators are 94,217
The GCF of 106,406 is 2 .
LCM of 94,217 is 20398.
The greatest common factor of 106/94,406/217 = [GCF of 106,406]/[LCM of 94,217]= 2/20398
Therefore, the GCF of 106/94,406/217 is 2/20398.
To find the highest common factor of 106,406, we have to find the factors of both numbers and list the highest common factor.
The factors of 106 are 1, 2, 53, 106
The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406
The HCF of 106,406 is 2.
Lets's calculate GCF of 106,406
| 2 | 106, 406 |
| 53, 203 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 106,406 By Matching Biggest Common Factor Method
Now, list down the factors of 106
:1,2,53,106
Now, list down the factors of 406
:1,2,7,14,29,58,203,406
Greatest Common Factor
We found the factors 106,406 . The biggest common factor number is the GCF number.
So the greatest common factor 106,406 is 2.
Lets's calculate LCM of 94,217
Given numbers has no common factors except 1. So, there LCM is their product i.e 20398
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/20398
Therefore, the GCF of Fractions 106/94,406/217 is 2/20398
Least Common Multiple of 94,217 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 94,217 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(94,217) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(94,217) x common factors =1 x 1 = 1
LCM(94,217) = ( 94 × 217 ) / 1
LCM(94,217) = 20398 / 1
LCM(94,217) = 20398
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 106/94, 406/217
1. What is the HCF of 106,406?
The HCF of 106,406 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 106/94, 406/217?
Answer: GCF of Numerators as per given numbers 106/94, 406/217 is
GCF of Numerators i.e. for 106,406 is 2
LCM of denominators i.e. for 94,217 is 20398.
Thus, GCF of Fractions is 2/20398.Finally, GCF of Fractions for 106/94, 406/217 is 2/20398.