GCF of 213/30, 219/5985
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 213/30, 219/5985 i.e 3/11970 easily. The following is the detailed procedure to determine the greatest common factor of fractions 213/30, 219/5985.
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 213/30,219/5985?
Given fractions are 213/30,219/5985
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 213/30,219/5985, numerators are 213,219
Denominators are 30,5985
The GCF of 213,219 is 3 .
LCM of 30,5985 is 11970.
The greatest common factor of 213/30,219/5985 = [GCF of 213,219]/[LCM of 30,5985]= 3/11970
Therefore, the GCF of 213/30,219/5985 is 3/11970.
To find the highest common factor of 213,219, 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 219 are 1, 3, 73, 219
The HCF of 213,219 is 3.
Lets's calculate GCF of 213,219
| 3 | 213, 219 |
| 71, 73 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 213,219 By Matching Biggest Common Factor Method
Now, list down the factors of 213
:1,3,71,213
Now, list down the factors of 219
:1,3,73,219
Greatest Common Factor
We found the factors 213,219 . The biggest common factor number is the GCF number.
So the greatest common factor 213,219 is 3.
Lets's calculate LCM of 30,5985
| 3 | 30, 5985 |
| 5 | 10, 1995 |
| 2, 399 |
∴ So the LCM of the given numbers is 3 x 5 x 2 x 399 = 11970
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/11970
Therefore, the GCF of Fractions 213/30,219/5985 is 3/11970
Least Common Multiple of 30,5985 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 30,5985 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,5985) = 15
common factors(in case of two or more numbers have common factors) = 1
GCF(30,5985) x common factors =15 x 1 = 15
LCM(30,5985) = ( 30 × 5985 ) / 15
LCM(30,5985) = 179550 / 15
LCM(30,5985) = 11970
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FAQs on GCF of Fractions of 213/30, 219/5985
1. What is the HCF of 213,219?
The HCF of 213,219 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 213/30, 219/5985?
Answer: GCF of Numerators as per given numbers 213/30, 219/5985 is
GCF of Numerators i.e. for 213,219 is 3
LCM of denominators i.e. for 30,5985 is 11970.
Thus, GCF of Fractions is 3/11970.Finally, GCF of Fractions for 213/30, 219/5985 is 3/11970.