GCF of 212/75, 421/58, 232/24
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 212/75, 421/58, 232/24 i.e 1/17400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 212/75, 421/58, 232/24.
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 212/75,421/58,232/24?
Given fractions are 212/75,421/58,232/24
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 212/75,421/58,232/24, numerators are 212,421,232
Denominators are 75,58,24
The GCF of 212,421,232 is 1 .
LCM of 75,58,24 is 17400.
The greatest common factor of 212/75,421/58,232/24 = [GCF of 212,421,232]/[LCM of 75,58,24]= 1/17400
Therefore, the GCF of 212/75,421/58,232/24 is 1/17400.
To find the highest common factor of 212,421,232, we have to find the factors of both numbers and list the highest common factor.
The factors of 212 are 1, 2, 4, 53, 106, 212
The factors of 421 are 1, 421
The factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232
The HCF of 212,421,232 is 1.
Lets's calculate GCF of 212,421,232
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 212,421,232 By Matching Biggest Common Factor Method
Now, list down the factors of 212
:1,2,4,53,106,212
Now, list down the factors of 421
:1,421
Now, list down the factors of 232
:1,2,4,8,29,58,116,232
Greatest Common Factor
We found the factors 212,421,232 . The biggest common factor number is the GCF number.
So the greatest common factor 212,421,232 is 1.
Lets's calculate LCM of 75,58,24
| 2 | 75, 58, 24 |
| 3 | 75, 29, 12 |
| 25, 29, 4 |
∴ So the LCM of the given numbers is 2 x 3 x 25 x 29 x 4 = 17400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17400
Therefore, the GCF of Fractions 212/75,421/58,232/24 is 1/17400
Least Common Multiple of 75,58,24 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 75,58,24 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,58,24) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(75,58,24) x common factors =1 x 6 = 6
LCM(75,58,24) = ( 75 × 58 × 24 ) / 6
LCM(75,58,24) = 104400 / 6
LCM(75,58,24) = 17400
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FAQs on GCF of Fractions of 212/75, 421/58, 232/24
1. What is the HCF of 212,421,232?
The HCF of 212,421,232 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 212/75, 421/58, 232/24?
Answer: GCF of Numerators as per given numbers 212/75, 421/58, 232/24 is
GCF of Numerators i.e. for 212,421,232 is 1
LCM of denominators i.e. for 75,58,24 is 17400.
Thus, GCF of Fractions is 1/17400.Finally, GCF of Fractions for 212/75, 421/58, 232/24 is 1/17400.