GCF of 384/342, 217/700
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 384/342, 217/700 i.e 1/119700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 384/342, 217/700.
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 384/342,217/700?
Given fractions are 384/342,217/700
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 384/342,217/700, numerators are 384,217
Denominators are 342,700
The GCF of 384,217 is 1 .
LCM of 342,700 is 119700.
The greatest common factor of 384/342,217/700 = [GCF of 384,217]/[LCM of 342,700]= 1/119700
Therefore, the GCF of 384/342,217/700 is 1/119700.
To find the highest common factor of 384,217, we have to find the factors of both numbers and list the highest common factor.
The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
The factors of 217 are 1, 7, 31, 217
The HCF of 384,217 is 1.
Lets's calculate GCF of 384,217
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 384,217 By Matching Biggest Common Factor Method
Now, list down the factors of 384
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384
Now, list down the factors of 217
:1,7,31,217
Greatest Common Factor
We found the factors 384,217 . The biggest common factor number is the GCF number.
So the greatest common factor 384,217 is 1.
Lets's calculate LCM of 342,700
| 2 | 342, 700 |
| 171, 350 |
∴ So the LCM of the given numbers is 2 x 171 x 350 = 119700
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/119700
Therefore, the GCF of Fractions 384/342,217/700 is 1/119700
Least Common Multiple of 342,700 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 342,700 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(342,700) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(342,700) x common factors =2 x 1 = 2
LCM(342,700) = ( 342 × 700 ) / 2
LCM(342,700) = 239400 / 2
LCM(342,700) = 119700
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 384/342, 217/700
1. What is the HCF of 384,217?
The HCF of 384,217 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 384/342, 217/700?
Answer: GCF of Numerators as per given numbers 384/342, 217/700 is
GCF of Numerators i.e. for 384,217 is 1
LCM of denominators i.e. for 342,700 is 119700.
Thus, GCF of Fractions is 1/119700.Finally, GCF of Fractions for 384/342, 217/700 is 1/119700.