GCF of 837/840, 874/723, 406/259
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 837/840, 874/723, 406/259 i.e 1/7490280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 837/840, 874/723, 406/259.
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 837/840,874/723,406/259?
Given fractions are 837/840,874/723,406/259
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 837/840,874/723,406/259, numerators are 837,874,406
Denominators are 840,723,259
The GCF of 837,874,406 is 1 .
LCM of 840,723,259 is 7490280.
The greatest common factor of 837/840,874/723,406/259 = [GCF of 837,874,406]/[LCM of 840,723,259]= 1/7490280
Therefore, the GCF of 837/840,874/723,406/259 is 1/7490280.
To find the highest common factor of 837,874,406, we have to find the factors of both numbers and list the highest common factor.
The factors of 837 are 1, 3, 9, 27, 31, 93, 279, 837
The factors of 874 are 1, 2, 19, 23, 38, 46, 437, 874
The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406
The HCF of 837,874,406 is 1.
Lets's calculate GCF of 837,874,406
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 837,874,406 By Matching Biggest Common Factor Method
Now, list down the factors of 837
:1,3,9,27,31,93,279,837
Now, list down the factors of 874
:1,2,19,23,38,46,437,874
Now, list down the factors of 406
:1,2,7,14,29,58,203,406
Greatest Common Factor
We found the factors 837,874,406 . The biggest common factor number is the GCF number.
So the greatest common factor 837,874,406 is 1.
Lets's calculate LCM of 840,723,259
| 3 | 840, 723, 259 |
| 7 | 280, 241, 259 |
| 40, 241, 37 |
∴ So the LCM of the given numbers is 3 x 7 x 40 x 241 x 37 = 7490280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7490280
Therefore, the GCF of Fractions 837/840,874/723,406/259 is 1/7490280
Least Common Multiple of 840,723,259 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 840,723,259 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(840,723,259) = 1
common factors(in case of two or more numbers have common factors) = 21
GCF(840,723,259) x common factors =1 x 21 = 21
LCM(840,723,259) = ( 840 × 723 × 259 ) / 21
LCM(840,723,259) = 157295880 / 21
LCM(840,723,259) = 7490280
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 837/840, 874/723, 406/259
1. What is the HCF of 837,874,406?
The HCF of 837,874,406 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 837/840, 874/723, 406/259?
Answer: GCF of Numerators as per given numbers 837/840, 874/723, 406/259 is
GCF of Numerators i.e. for 837,874,406 is 1
LCM of denominators i.e. for 840,723,259 is 7490280.
Thus, GCF of Fractions is 1/7490280.Finally, GCF of Fractions for 837/840, 874/723, 406/259 is 1/7490280.