GCF of 370/18, 509/122
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 370/18, 509/122 i.e 1/1098 easily. The following is the detailed procedure to determine the greatest common factor of fractions 370/18, 509/122.
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 370/18,509/122?
Given fractions are 370/18,509/122
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 370/18,509/122, numerators are 370,509
Denominators are 18,122
The GCF of 370,509 is 1 .
LCM of 18,122 is 1098.
The greatest common factor of 370/18,509/122 = [GCF of 370,509]/[LCM of 18,122]= 1/1098
Therefore, the GCF of 370/18,509/122 is 1/1098.
To find the highest common factor of 370,509, we have to find the factors of both numbers and list the highest common factor.
The factors of 370 are 1, 2, 5, 10, 37, 74, 185, 370
The factors of 509 are 1, 509
The HCF of 370,509 is 1.
Lets's calculate GCF of 370,509
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 370,509 By Matching Biggest Common Factor Method
Now, list down the factors of 370
:1,2,5,10,37,74,185,370
Now, list down the factors of 509
:1,509
Greatest Common Factor
We found the factors 370,509 . The biggest common factor number is the GCF number.
So the greatest common factor 370,509 is 1.
Lets's calculate LCM of 18,122
| 2 | 18, 122 |
| 9, 61 |
∴ So the LCM of the given numbers is 2 x 9 x 61 = 1098
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1098
Therefore, the GCF of Fractions 370/18,509/122 is 1/1098
Least Common Multiple of 18,122 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 18,122 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(18,122) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(18,122) x common factors =2 x 1 = 2
LCM(18,122) = ( 18 × 122 ) / 2
LCM(18,122) = 2196 / 2
LCM(18,122) = 1098
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 370/18, 509/122
1. What is the HCF of 370,509?
The HCF of 370,509 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 370/18, 509/122?
Answer: GCF of Numerators as per given numbers 370/18, 509/122 is
GCF of Numerators i.e. for 370,509 is 1
LCM of denominators i.e. for 18,122 is 1098.
Thus, GCF of Fractions is 1/1098.Finally, GCF of Fractions for 370/18, 509/122 is 1/1098.