GCF of 30/16, 40/81, 610/634
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 30/16, 40/81, 610/634 i.e 10/410832 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/16, 40/81, 610/634.
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 30/16,40/81,610/634?
Given fractions are 30/16,40/81,610/634
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 30/16,40/81,610/634, numerators are 30,40,610
Denominators are 16,81,634
The GCF of 30,40,610 is 10 .
LCM of 16,81,634 is 410832.
The greatest common factor of 30/16,40/81,610/634 = [GCF of 30,40,610]/[LCM of 16,81,634]= 10/410832
Therefore, the GCF of 30/16,40/81,610/634 is 10/410832.
To find the highest common factor of 30,40,610, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 610 are 1, 2, 5, 10, 61, 122, 305, 610
The HCF of 30,40,610 is 10.
Lets's calculate GCF of 30,40,610
| 2 | 30, 40, 610 |
| 5 | 15, 20, 305 |
| 3, 4, 61 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 30,40,610 By Matching Biggest Common Factor Method
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 610
:1,2,5,10,61,122,305,610
Greatest Common Factor
We found the factors 30,40,610 . The biggest common factor number is the GCF number.
So the greatest common factor 30,40,610 is 10.
Lets's calculate LCM of 16,81,634
| 2 | 16, 81, 634 |
| 8, 81, 317 |
∴ So the LCM of the given numbers is 2 x 8 x 81 x 317 = 410832
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/410832
Therefore, the GCF of Fractions 30/16,40/81,610/634 is 10/410832
Least Common Multiple of 16,81,634 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 16,81,634 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(16,81,634) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(16,81,634) x common factors =1 x 2 = 2
LCM(16,81,634) = ( 16 × 81 × 634 ) / 2
LCM(16,81,634) = 821664 / 2
LCM(16,81,634) = 410832
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FAQs on GCF of Fractions of 30/16, 40/81, 610/634
1. What is the HCF of 30,40,610?
The HCF of 30,40,610 is 10
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 30/16, 40/81, 610/634?
Answer: GCF of Numerators as per given numbers 30/16, 40/81, 610/634 is
GCF of Numerators i.e. for 30,40,610 is 10
LCM of denominators i.e. for 16,81,634 is 410832.
Thus, GCF of Fractions is 10/410832.Finally, GCF of Fractions for 30/16, 40/81, 610/634 is 10/410832.