GCF of 105/36, 150/54, 210/126
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, 150/54, 210/126 i.e 15/756 easily. The following is the detailed procedure to determine the greatest common factor of fractions 105/36, 150/54, 210/126.
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 105/36,150/54,210/126?
Given fractions are 105/36,150/54,210/126
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 105/36,150/54,210/126, numerators are 105,150,210
Denominators are 36,54,126
The GCF of 105,150,210 is 15 .
LCM of 36,54,126 is 756.
The greatest common factor of 105/36,150/54,210/126 = [GCF of 105,150,210]/[LCM of 36,54,126]= 15/756
Therefore, the GCF of 105/36,150/54,210/126 is 15/756.
To find the highest common factor of 105,150,210, 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 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The HCF of 105,150,210 is 15.
Lets's calculate GCF of 105,150,210
| 3 | 105, 150, 210 |
| 5 | 35, 50, 70 |
| 7, 10, 14 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 105,150,210 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 150
:1,2,3,5,6,10,15,25,30,50,75,150
Now, list down the factors of 210
:1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
Greatest Common Factor
We found the factors 105,150,210 . The biggest common factor number is the GCF number.
So the greatest common factor 105,150,210 is 15.
Lets's calculate LCM of 36,54,126
| 2 | 36, 54, 126 |
| 3 | 18, 27, 63 |
| 3 | 6, 9, 21 |
| 2, 3, 7 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 2 x 3 x 7 = 756
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/756
Therefore, the GCF of Fractions 105/36,150/54,210/126 is 15/756
Least Common Multiple of 36,54,126 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 36,54,126 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(36,54,126) = 18
common factors(in case of two or more numbers have common factors) = 18
GCF(36,54,126) x common factors =18 x 18 = 324
LCM(36,54,126) = ( 36 × 54 × 126 ) / 324
LCM(36,54,126) = 244944 / 324
LCM(36,54,126) = 756
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 105/36, 150/54, 210/126
1. What is the HCF of 105,150,210?
The HCF of 105,150,210 is 15
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, 150/54, 210/126?
Answer: GCF of Numerators as per given numbers 105/36, 150/54, 210/126 is
GCF of Numerators i.e. for 105,150,210 is 15
LCM of denominators i.e. for 36,54,126 is 756.
Thus, GCF of Fractions is 15/756.Finally, GCF of Fractions for 105/36, 150/54, 210/126 is 15/756.