GCF of 621/90, 684/20, 453/12
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 621/90, 684/20, 453/12 i.e 3/180 easily. The following is the detailed procedure to determine the greatest common factor of fractions 621/90, 684/20, 453/12.
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 621/90,684/20,453/12?
Given fractions are 621/90,684/20,453/12
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 621/90,684/20,453/12, numerators are 621,684,453
Denominators are 90,20,12
The GCF of 621,684,453 is 3 .
LCM of 90,20,12 is 180.
The greatest common factor of 621/90,684/20,453/12 = [GCF of 621,684,453]/[LCM of 90,20,12]= 3/180
Therefore, the GCF of 621/90,684/20,453/12 is 3/180.
To find the highest common factor of 621,684,453, we have to find the factors of both numbers and list the highest common factor.
The factors of 621 are 1, 3, 9, 23, 27, 69, 207, 621
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The factors of 453 are 1, 3, 151, 453
The HCF of 621,684,453 is 3.
Lets's calculate GCF of 621,684,453
| 3 | 621, 684, 453 |
| 207, 228, 151 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 621,684,453 By Matching Biggest Common Factor Method
Now, list down the factors of 621
:1,3,9,23,27,69,207,621
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Now, list down the factors of 453
:1,3,151,453
Greatest Common Factor
We found the factors 621,684,453 . The biggest common factor number is the GCF number.
So the greatest common factor 621,684,453 is 3.
Lets's calculate LCM of 90,20,12
| 2 | 90, 20, 12 |
| 2 | 45, 10, 6 |
| 3 | 45, 5, 3 |
| 5 | 15, 5, 1 |
| 3, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 3 x 1 x 1 = 180
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/180
Therefore, the GCF of Fractions 621/90,684/20,453/12 is 3/180
Least Common Multiple of 90,20,12 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 90,20,12 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(90,20,12) = 2
common factors(in case of two or more numbers have common factors) = 60
GCF(90,20,12) x common factors =2 x 60 = 120
LCM(90,20,12) = ( 90 × 20 × 12 ) / 120
LCM(90,20,12) = 21600 / 120
LCM(90,20,12) = 180
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FAQs on GCF of Fractions of 621/90, 684/20, 453/12
1. What is the HCF of 621,684,453?
The HCF of 621,684,453 is 3
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 621/90, 684/20, 453/12?
Answer: GCF of Numerators as per given numbers 621/90, 684/20, 453/12 is
GCF of Numerators i.e. for 621,684,453 is 3
LCM of denominators i.e. for 90,20,12 is 180.
Thus, GCF of Fractions is 3/180.Finally, GCF of Fractions for 621/90, 684/20, 453/12 is 3/180.