GCF of 395/12, 214/100
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 395/12, 214/100 i.e 1/300 easily. The following is the detailed procedure to determine the greatest common factor of fractions 395/12, 214/100.
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 395/12,214/100?
Given fractions are 395/12,214/100
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 395/12,214/100, numerators are 395,214
Denominators are 12,100
The GCF of 395,214 is 1 .
LCM of 12,100 is 300.
The greatest common factor of 395/12,214/100 = [GCF of 395,214]/[LCM of 12,100]= 1/300
Therefore, the GCF of 395/12,214/100 is 1/300.
To find the highest common factor of 395,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 395 are 1, 5, 79, 395
The factors of 214 are 1, 2, 107, 214
The HCF of 395,214 is 1.
Lets's calculate GCF of 395,214
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 395,214 By Matching Biggest Common Factor Method
Now, list down the factors of 395
:1,5,79,395
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 395,214 . The biggest common factor number is the GCF number.
So the greatest common factor 395,214 is 1.
Lets's calculate LCM of 12,100
| 2 | 12, 100 |
| 2 | 6, 50 |
| 3, 25 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 25 = 300
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/300
Therefore, the GCF of Fractions 395/12,214/100 is 1/300
Least Common Multiple of 12,100 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 12,100 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,100) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(12,100) x common factors =4 x 1 = 4
LCM(12,100) = ( 12 × 100 ) / 4
LCM(12,100) = 1200 / 4
LCM(12,100) = 300
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FAQs on GCF of Fractions of 395/12, 214/100
1. What is the HCF of 395,214?
The HCF of 395,214 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 395/12, 214/100?
Answer: GCF of Numerators as per given numbers 395/12, 214/100 is
GCF of Numerators i.e. for 395,214 is 1
LCM of denominators i.e. for 12,100 is 300.
Thus, GCF of Fractions is 1/300.Finally, GCF of Fractions for 395/12, 214/100 is 1/300.