GCF of 43/32, 969/60, 814/198
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 43/32, 969/60, 814/198 i.e 1/15840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 43/32, 969/60, 814/198.
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 43/32,969/60,814/198?
Given fractions are 43/32,969/60,814/198
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 43/32,969/60,814/198, numerators are 43,969,814
Denominators are 32,60,198
The GCF of 43,969,814 is 1 .
LCM of 32,60,198 is 15840.
The greatest common factor of 43/32,969/60,814/198 = [GCF of 43,969,814]/[LCM of 32,60,198]= 1/15840
Therefore, the GCF of 43/32,969/60,814/198 is 1/15840.
To find the highest common factor of 43,969,814, we have to find the factors of both numbers and list the highest common factor.
The factors of 43 are 1, 43
The factors of 969 are 1, 3, 17, 19, 51, 57, 323, 969
The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814
The HCF of 43,969,814 is 1.
Lets's calculate GCF of 43,969,814
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 43,969,814 By Matching Biggest Common Factor Method
Now, list down the factors of 43
:1,43
Now, list down the factors of 969
:1,3,17,19,51,57,323,969
Now, list down the factors of 814
:1,2,11,22,37,74,407,814
Greatest Common Factor
We found the factors 43,969,814 . The biggest common factor number is the GCF number.
So the greatest common factor 43,969,814 is 1.
Lets's calculate LCM of 32,60,198
| 2 | 32, 60, 198 |
| 2 | 16, 30, 99 |
| 3 | 8, 15, 99 |
| 8, 5, 33 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 8 x 5 x 33 = 15840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15840
Therefore, the GCF of Fractions 43/32,969/60,814/198 is 1/15840
Least Common Multiple of 32,60,198 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 32,60,198 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,60,198) = 2
common factors(in case of two or more numbers have common factors) = 12
GCF(32,60,198) x common factors =2 x 12 = 24
LCM(32,60,198) = ( 32 × 60 × 198 ) / 24
LCM(32,60,198) = 380160 / 24
LCM(32,60,198) = 15840
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 43/32, 969/60, 814/198
1. What is the HCF of 43,969,814?
The HCF of 43,969,814 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 43/32, 969/60, 814/198?
Answer: GCF of Numerators as per given numbers 43/32, 969/60, 814/198 is
GCF of Numerators i.e. for 43,969,814 is 1
LCM of denominators i.e. for 32,60,198 is 15840.
Thus, GCF of Fractions is 1/15840.Finally, GCF of Fractions for 43/32, 969/60, 814/198 is 1/15840.