GCF of 237/132, 213/324
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 237/132, 213/324 i.e 3/3564 easily. The following is the detailed procedure to determine the greatest common factor of fractions 237/132, 213/324.
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 237/132,213/324?
Given fractions are 237/132,213/324
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 237/132,213/324, numerators are 237,213
Denominators are 132,324
The GCF of 237,213 is 3 .
LCM of 132,324 is 3564.
The greatest common factor of 237/132,213/324 = [GCF of 237,213]/[LCM of 132,324]= 3/3564
Therefore, the GCF of 237/132,213/324 is 3/3564.
To find the highest common factor of 237,213, we have to find the factors of both numbers and list the highest common factor.
The factors of 237 are 1, 3, 79, 237
The factors of 213 are 1, 3, 71, 213
The HCF of 237,213 is 3.
Lets's calculate GCF of 237,213
| 3 | 237, 213 |
| 79, 71 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 237,213 By Matching Biggest Common Factor Method
Now, list down the factors of 237
:1,3,79,237
Now, list down the factors of 213
:1,3,71,213
Greatest Common Factor
We found the factors 237,213 . The biggest common factor number is the GCF number.
So the greatest common factor 237,213 is 3.
Lets's calculate LCM of 132,324
| 2 | 132, 324 |
| 2 | 66, 162 |
| 3 | 33, 81 |
| 11, 27 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 11 x 27 = 3564
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/3564
Therefore, the GCF of Fractions 237/132,213/324 is 3/3564
Least Common Multiple of 132,324 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 132,324 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(132,324) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(132,324) x common factors =12 x 1 = 12
LCM(132,324) = ( 132 × 324 ) / 12
LCM(132,324) = 42768 / 12
LCM(132,324) = 3564
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FAQs on GCF of Fractions of 237/132, 213/324
1. What is the HCF of 237,213?
The HCF of 237,213 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 237/132, 213/324?
Answer: GCF of Numerators as per given numbers 237/132, 213/324 is
GCF of Numerators i.e. for 237,213 is 3
LCM of denominators i.e. for 132,324 is 3564.
Thus, GCF of Fractions is 3/3564.Finally, GCF of Fractions for 237/132, 213/324 is 3/3564.