GCF of 8/23, 53/69, 12/212, 172/660
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8/23, 53/69, 12/212, 172/660 i.e 1/804540 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8/23, 53/69, 12/212, 172/660.
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 8/23,53/69,12/212,172/660?
Given fractions are 8/23,53/69,12/212,172/660
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 8/23,53/69,12/212,172/660, numerators are 8,53,12,172
Denominators are 23,69,212,660
The GCF of 8,53,12,172 is 1 .
LCM of 23,69,212,660 is 804540.
The greatest common factor of 8/23,53/69,12/212,172/660 = [GCF of 8,53,12,172]/[LCM of 23,69,212,660]= 1/804540
Therefore, the GCF of 8/23,53/69,12/212,172/660 is 1/804540.
To find the highest common factor of 8,53,12,172, we have to find the factors of both numbers and list the highest common factor.
The factors of 8 are 1, 2, 4, 8
The factors of 53 are 1, 53
The factors of 12 are 1, 2, 3, 4, 6, 12
The factors of 172 are 1, 2, 4, 43, 86, 172
The HCF of 8,53,12,172 is 1.
Lets's calculate GCF of 8,53,12,172
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 8,53,12,172 By Matching Biggest Common Factor Method
Now, list down the factors of 8
:1,2,4,8
Now, list down the factors of 53
:1,53
Now, list down the factors of 12
:1,2,3,4,6,12
Now, list down the factors of 172
:1,2,4,43,86,172
Greatest Common Factor
We found the factors 8,53,12,172 . The biggest common factor number is the GCF number.
So the greatest common factor 8,53,12,172 is 1.
Lets's calculate LCM of 23,69,212,660
| 2 | 23, 69, 212, 660 |
| 2 | 23, 69, 106, 330 |
| 3 | 23, 69, 53, 165 |
| 23 | 23, 23, 53, 55 |
| 1, 1, 53, 55 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 23 x 1 x 1 x 53 x 55 = 804540
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/804540
Therefore, the GCF of Fractions 8/23,53/69,12/212,172/660 is 1/804540
Least Common Multiple of 23,69,212,660 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 23,69,212,660 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(23,69,212,660) = 1
common factors(in case of two or more numbers have common factors) = 276
GCF(23,69,212,660) x common factors =1 x 276 = 276
LCM(23,69,212,660) = ( 23 × 69 × 212 × 660 ) / 276
LCM(23,69,212,660) = 222053040 / 276
LCM(23,69,212,660) = 804540
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 8/23, 53/69, 12/212, 172/660
1. What is the HCF of 8,53,12,172?
The HCF of 8,53,12,172 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 8/23, 53/69, 12/212, 172/660?
Answer: GCF of Numerators as per given numbers 8/23, 53/69, 12/212, 172/660 is
GCF of Numerators i.e. for 8,53,12,172 is 1
LCM of denominators i.e. for 23,69,212,660 is 804540.
Thus, GCF of Fractions is 1/804540.Finally, GCF of Fractions for 8/23, 53/69, 12/212, 172/660 is 1/804540.