GCF of 345/23, 990/66, 774/40
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 345/23, 990/66, 774/40 i.e 3/30360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 345/23, 990/66, 774/40.
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 345/23,990/66,774/40?
Given fractions are 345/23,990/66,774/40
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 345/23,990/66,774/40, numerators are 345,990,774
Denominators are 23,66,40
The GCF of 345,990,774 is 3 .
LCM of 23,66,40 is 30360.
The greatest common factor of 345/23,990/66,774/40 = [GCF of 345,990,774]/[LCM of 23,66,40]= 3/30360
Therefore, the GCF of 345/23,990/66,774/40 is 3/30360.
To find the highest common factor of 345,990,774, we have to find the factors of both numbers and list the highest common factor.
The factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345
The factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990
The factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774
The HCF of 345,990,774 is 3.
Lets's calculate GCF of 345,990,774
| 3 | 345, 990, 774 |
| 115, 330, 258 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 345,990,774 By Matching Biggest Common Factor Method
Now, list down the factors of 345
:1,3,5,15,23,69,115,345
Now, list down the factors of 990
:1,2,3,5,6,9,10,11,15,18,22,30,33,45,55,66,90,99,110,165,198,330,495,990
Now, list down the factors of 774
:1,2,3,6,9,18,43,86,129,258,387,774
Greatest Common Factor
We found the factors 345,990,774 . The biggest common factor number is the GCF number.
So the greatest common factor 345,990,774 is 3.
Lets's calculate LCM of 23,66,40
| 2 | 23, 66, 40 |
| 23, 33, 20 |
∴ So the LCM of the given numbers is 2 x 23 x 33 x 20 = 30360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/30360
Therefore, the GCF of Fractions 345/23,990/66,774/40 is 3/30360
Least Common Multiple of 23,66,40 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 23,66,40 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(23,66,40) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(23,66,40) x common factors =1 x 2 = 2
LCM(23,66,40) = ( 23 × 66 × 40 ) / 2
LCM(23,66,40) = 60720 / 2
LCM(23,66,40) = 30360
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FAQs on GCF of Fractions of 345/23, 990/66, 774/40
1. What is the HCF of 345,990,774?
The HCF of 345,990,774 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 345/23, 990/66, 774/40?
Answer: GCF of Numerators as per given numbers 345/23, 990/66, 774/40 is
GCF of Numerators i.e. for 345,990,774 is 3
LCM of denominators i.e. for 23,66,40 is 30360.
Thus, GCF of Fractions is 3/30360.Finally, GCF of Fractions for 345/23, 990/66, 774/40 is 3/30360.