GCF of 213/180, 810/756
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 213/180, 810/756 i.e 3/3780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 213/180, 810/756.
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 213/180,810/756?
Given fractions are 213/180,810/756
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 213/180,810/756, numerators are 213,810
Denominators are 180,756
The GCF of 213,810 is 3 .
LCM of 180,756 is 3780.
The greatest common factor of 213/180,810/756 = [GCF of 213,810]/[LCM of 180,756]= 3/3780
Therefore, the GCF of 213/180,810/756 is 3/3780.
To find the highest common factor of 213,810, we have to find the factors of both numbers and list the highest common factor.
The factors of 213 are 1, 3, 71, 213
The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810
The HCF of 213,810 is 3.
Lets's calculate GCF of 213,810
| 3 | 213, 810 |
| 71, 270 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 213,810 By Matching Biggest Common Factor Method
Now, list down the factors of 213
:1,3,71,213
Now, list down the factors of 810
:1,2,3,5,6,9,10,15,18,27,30,45,54,81,90,135,162,270,405,810
Greatest Common Factor
We found the factors 213,810 . The biggest common factor number is the GCF number.
So the greatest common factor 213,810 is 3.
Lets's calculate LCM of 180,756
| 2 | 180, 756 |
| 2 | 90, 378 |
| 3 | 45, 189 |
| 3 | 15, 63 |
| 5, 21 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 5 x 21 = 3780
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/3780
Therefore, the GCF of Fractions 213/180,810/756 is 3/3780
Least Common Multiple of 180,756 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 180,756 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(180,756) = 36
common factors(in case of two or more numbers have common factors) = 1
GCF(180,756) x common factors =36 x 1 = 36
LCM(180,756) = ( 180 × 756 ) / 36
LCM(180,756) = 136080 / 36
LCM(180,756) = 3780
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FAQs on GCF of Fractions of 213/180, 810/756
1. What is the HCF of 213,810?
The HCF of 213,810 is 3
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 213/180, 810/756?
Answer: GCF of Numerators as per given numbers 213/180, 810/756 is
GCF of Numerators i.e. for 213,810 is 3
LCM of denominators i.e. for 180,756 is 3780.
Thus, GCF of Fractions is 3/3780.Finally, GCF of Fractions for 213/180, 810/756 is 3/3780.