Use our free GCF of Fractions Calculator tool to compute the GCF of 836/116, 405/130 i.e 1/7540 easily. The following is the detailed procedure to determine the greatest common factor of fractions 836/116, 405/130.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 836/116,405/130
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 836/116,405/130, numerators are 836,405
Denominators are 116,130
The GCF of 836,405 is 1 .
LCM of 116,130 is 7540.
The greatest common factor of 836/116,405/130 = [GCF of 836,405]/[LCM of 116,130]= 1/7540
Therefore, the GCF of 836/116,405/130 is 1/7540.
To find the highest common factor of 836,405, we have to find the factors of both numbers and list the highest common factor.
The factors of 836 are 1, 2, 4, 11, 19, 22, 38, 44, 76, 209, 418, 836
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The HCF of 836,405 is 1.
Lets's calculate GCF of 836,405
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 836
:1,2,4,11,19,22,38,44,76,209,418,836
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Greatest Common Factor
We found the factors 836,405 . The biggest common factor number is the GCF number.
So the greatest common factor 836,405 is 1.
Lets's calculate LCM of 116,130
2 | 116, 130 |
58, 65 |
∴ So the LCM of the given numbers is 2 x 58 x 65 = 7540
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7540
Therefore, the GCF of Fractions 836/116,405/130 is 1/7540
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 116,130 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(116,130) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(116,130) x common factors =2 x 1 = 2
LCM(116,130) = ( 116 × 130 ) / 2
LCM(116,130) = 15080 / 2
LCM(116,130) = 7540
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 836,405?
The HCF of 836,405 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 836/116, 405/130?
Answer: GCF of Numerators as per given numbers 836/116, 405/130 is
GCF of Numerators i.e. for 836,405 is 1
LCM of denominators i.e. for 116,130 is 7540.
Thus, GCF of Fractions is 1/7540.Finally, GCF of Fractions for 836/116, 405/130 is 1/7540.