Use our free GCF of Fractions Calculator tool to compute the GCF of 17/236, 61/3658 i.e 1/7316 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/236, 61/3658.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 17/236,61/3658
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 17/236,61/3658, numerators are 17,61
Denominators are 236,3658
The GCF of 17,61 is 1 .
LCM of 236,3658 is 7316.
The greatest common factor of 17/236,61/3658 = [GCF of 17,61]/[LCM of 236,3658]= 1/7316
Therefore, the GCF of 17/236,61/3658 is 1/7316.
To find the highest common factor of 17,61, we have to find the factors of both numbers and list the highest common factor.
The factors of 17 are 1, 17
The factors of 61 are 1, 61
The HCF of 17,61 is 1.
Lets's calculate GCF of 17,61
∴ So GCF of numbers is 1 because of no common factors present between them.
Lets's calculate LCM of 236,3658
2 | 236, 3658 |
59 | 118, 1829 |
2, 31 |
∴ So the LCM of the given numbers is 2 x 59 x 2 x 31 = 7316
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7316
Therefore, the GCF of Fractions 17/236,61/3658 is 1/7316
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 236,3658 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(236,3658) = 118
common factors(in case of two or more numbers have common factors) = 1
GCF(236,3658) x common factors =118 x 1 = 118
LCM(236,3658) = ( 236 × 3658 ) / 118
LCM(236,3658) = 863288 / 118
LCM(236,3658) = 7316
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 17,61?
The HCF of 17,61 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 17/236, 61/3658?
Answer: GCF of Numerators as per given numbers 17/236, 61/3658 is
GCF of Numerators i.e. for 17,61 is 1
LCM of denominators i.e. for 236,3658 is 7316.
Thus, GCF of Fractions is 1/7316.Finally, GCF of Fractions for 17/236, 61/3658 is 1/7316.