GCF of 2/35, 30/63, 42/311, 731/259
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2/35, 30/63, 42/311, 731/259 i.e 1/3624705 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2/35, 30/63, 42/311, 731/259.
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 2/35,30/63,42/311,731/259?
Given fractions are 2/35,30/63,42/311,731/259
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 2/35,30/63,42/311,731/259, numerators are 2,30,42,731
Denominators are 35,63,311,259
The GCF of 2,30,42,731 is 1 .
LCM of 35,63,311,259 is 3624705.
The greatest common factor of 2/35,30/63,42/311,731/259 = [GCF of 2,30,42,731]/[LCM of 35,63,311,259]= 1/3624705
Therefore, the GCF of 2/35,30/63,42/311,731/259 is 1/3624705.
To find the highest common factor of 2,30,42,731, we have to find the factors of both numbers and list the highest common factor.
The factors of 2 are 1, 2
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 731 are 1, 17, 43, 731
The HCF of 2,30,42,731 is 1.
Lets's calculate GCF of 2,30,42,731
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 2,30,42,731 By Matching Biggest Common Factor Method
Now, list down the factors of 2
:1,2
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 731
:1,17,43,731
Greatest Common Factor
We found the factors 2,30,42,731 . The biggest common factor number is the GCF number.
So the greatest common factor 2,30,42,731 is 1.
Lets's calculate LCM of 35,63,311,259
| 7 | 35, 63, 311, 259 |
| 5, 9, 311, 37 |
∴ So the LCM of the given numbers is 7 x 5 x 9 x 311 x 37 = 3624705
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3624705
Therefore, the GCF of Fractions 2/35,30/63,42/311,731/259 is 1/3624705
Least Common Multiple of 35,63,311,259 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 35,63,311,259 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(35,63,311,259) = 1
common factors(in case of two or more numbers have common factors) = 49
GCF(35,63,311,259) x common factors =1 x 49 = 49
LCM(35,63,311,259) = ( 35 × 63 × 311 × 259 ) / 49
LCM(35,63,311,259) = 177610545 / 49
LCM(35,63,311,259) = 3624705
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 2/35, 30/63, 42/311, 731/259
1. What is the HCF of 2,30,42,731?
The HCF of 2,30,42,731 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 2/35, 30/63, 42/311, 731/259?
Answer: GCF of Numerators as per given numbers 2/35, 30/63, 42/311, 731/259 is
GCF of Numerators i.e. for 2,30,42,731 is 1
LCM of denominators i.e. for 35,63,311,259 is 3624705.
Thus, GCF of Fractions is 1/3624705.Finally, GCF of Fractions for 2/35, 30/63, 42/311, 731/259 is 1/3624705.