Use our free GCF of Fractions Calculator tool to compute the GCF of 5/61, 17/61, 10/385, 540/175 i.e 1/117425 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5/61, 17/61, 10/385, 540/175.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 5/61,17/61,10/385,540/175
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 5/61,17/61,10/385,540/175, numerators are 5,17,10,540
Denominators are 61,61,385,175
The GCF of 5,17,10,540 is 1 .
LCM of 61,61,385,175 is 117425.
The greatest common factor of 5/61,17/61,10/385,540/175 = [GCF of 5,17,10,540]/[LCM of 61,61,385,175]= 1/117425
Therefore, the GCF of 5/61,17/61,10/385,540/175 is 1/117425.
To find the highest common factor of 5,17,10,540, we have to find the factors of both numbers and list the highest common factor.
The factors of 5 are 1, 5
The factors of 17 are 1, 17
The factors of 10 are 1, 2, 5, 10
The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
The HCF of 5,17,10,540 is 1.
Lets's calculate GCF of 5,17,10,540
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 5
:1,5
Now, list down the factors of 17
:1,17
Now, list down the factors of 10
:1,2,5,10
Now, list down the factors of 540
:1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540
Greatest Common Factor
We found the factors 5,17,10,540 . The biggest common factor number is the GCF number.
So the greatest common factor 5,17,10,540 is 1.
Lets's calculate LCM of 61,61,385,175
5 | 61, 61, 385, 175 |
7 | 61, 61, 77, 35 |
61 | 61, 61, 11, 5 |
1, 1, 11, 5 |
∴ So the LCM of the given numbers is 5 x 7 x 61 x 1 x 1 x 11 x 5 = 117425
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/117425
Therefore, the GCF of Fractions 5/61,17/61,10/385,540/175 is 1/117425
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 61,61,385,175 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(61,61,385,175) = 1
common factors(in case of two or more numbers have common factors) = 2135
GCF(61,61,385,175) x common factors =1 x 2135 = 2135
LCM(61,61,385,175) = ( 61 × 61 × 385 × 175 ) / 2135
LCM(61,61,385,175) = 250702375 / 2135
LCM(61,61,385,175) = 117425
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 5,17,10,540?
The HCF of 5,17,10,540 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 5/61, 17/61, 10/385, 540/175?
Answer: GCF of Numerators as per given numbers 5/61, 17/61, 10/385, 540/175 is
GCF of Numerators i.e. for 5,17,10,540 is 1
LCM of denominators i.e. for 61,61,385,175 is 117425.
Thus, GCF of Fractions is 1/117425.Finally, GCF of Fractions for 5/61, 17/61, 10/385, 540/175 is 1/117425.