GCF of 40/678, 37/468, 659/650
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 40/678, 37/468, 659/650 i.e 1/1322100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/678, 37/468, 659/650.
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 40/678,37/468,659/650?
Given fractions are 40/678,37/468,659/650
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 40/678,37/468,659/650, numerators are 40,37,659
Denominators are 678,468,650
The GCF of 40,37,659 is 1 .
LCM of 678,468,650 is 1322100.
The greatest common factor of 40/678,37/468,659/650 = [GCF of 40,37,659]/[LCM of 678,468,650]= 1/1322100
Therefore, the GCF of 40/678,37/468,659/650 is 1/1322100.
To find the highest common factor of 40,37,659, we have to find the factors of both numbers and list the highest common factor.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 37 are 1, 37
The factors of 659 are 1, 659
The HCF of 40,37,659 is 1.
Lets's calculate GCF of 40,37,659
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 40,37,659 By Matching Biggest Common Factor Method
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 37
:1,37
Now, list down the factors of 659
:1,659
Greatest Common Factor
We found the factors 40,37,659 . The biggest common factor number is the GCF number.
So the greatest common factor 40,37,659 is 1.
Lets's calculate LCM of 678,468,650
| 2 | 678, 468, 650 |
| 3 | 339, 234, 325 |
| 13 | 113, 78, 325 |
| 113, 6, 25 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 113 x 6 x 25 = 1322100
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1322100
Therefore, the GCF of Fractions 40/678,37/468,659/650 is 1/1322100
Least Common Multiple of 678,468,650 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 678,468,650 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(678,468,650) = 2
common factors(in case of two or more numbers have common factors) = 78
GCF(678,468,650) x common factors =2 x 78 = 156
LCM(678,468,650) = ( 678 × 468 × 650 ) / 156
LCM(678,468,650) = 206247600 / 156
LCM(678,468,650) = 1322100
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 40/678, 37/468, 659/650
1. What is the HCF of 40,37,659?
The HCF of 40,37,659 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 40/678, 37/468, 659/650?
Answer: GCF of Numerators as per given numbers 40/678, 37/468, 659/650 is
GCF of Numerators i.e. for 40,37,659 is 1
LCM of denominators i.e. for 678,468,650 is 1322100.
Thus, GCF of Fractions is 1/1322100.Finally, GCF of Fractions for 40/678, 37/468, 659/650 is 1/1322100.