GCF of 105/36, 211/102
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 105/36, 211/102 i.e 1/612 easily. The following is the detailed procedure to determine the greatest common factor of fractions 105/36, 211/102.
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 105/36,211/102?
Given fractions are 105/36,211/102
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 105/36,211/102, numerators are 105,211
Denominators are 36,102
The GCF of 105,211 is 1 .
LCM of 36,102 is 612.
The greatest common factor of 105/36,211/102 = [GCF of 105,211]/[LCM of 36,102]= 1/612
Therefore, the GCF of 105/36,211/102 is 1/612.
To find the highest common factor of 105,211, we have to find the factors of both numbers and list the highest common factor.
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The factors of 211 are 1, 211
The HCF of 105,211 is 1.
Lets's calculate GCF of 105,211
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 105,211 By Matching Biggest Common Factor Method
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Now, list down the factors of 211
:1,211
Greatest Common Factor
We found the factors 105,211 . The biggest common factor number is the GCF number.
So the greatest common factor 105,211 is 1.
Lets's calculate LCM of 36,102
| 2 | 36, 102 |
| 3 | 18, 51 |
| 6, 17 |
∴ So the LCM of the given numbers is 2 x 3 x 6 x 17 = 612
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/612
Therefore, the GCF of Fractions 105/36,211/102 is 1/612
Least Common Multiple of 36,102 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 36,102 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(36,102) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(36,102) x common factors =6 x 1 = 6
LCM(36,102) = ( 36 × 102 ) / 6
LCM(36,102) = 3672 / 6
LCM(36,102) = 612
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 105/36, 211/102
1. What is the HCF of 105,211?
The HCF of 105,211 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 105/36, 211/102?
Answer: GCF of Numerators as per given numbers 105/36, 211/102 is
GCF of Numerators i.e. for 105,211 is 1
LCM of denominators i.e. for 36,102 is 612.
Thus, GCF of Fractions is 1/612.Finally, GCF of Fractions for 105/36, 211/102 is 1/612.