GCF of 986/37, 165/219
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 986/37, 165/219 i.e 1/8103 easily. The following is the detailed procedure to determine the greatest common factor of fractions 986/37, 165/219.
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 986/37,165/219?
Given fractions are 986/37,165/219
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 986/37,165/219, numerators are 986,165
Denominators are 37,219
The GCF of 986,165 is 1 .
LCM of 37,219 is 8103.
The greatest common factor of 986/37,165/219 = [GCF of 986,165]/[LCM of 37,219]= 1/8103
Therefore, the GCF of 986/37,165/219 is 1/8103.
To find the highest common factor of 986,165, we have to find the factors of both numbers and list the highest common factor.
The factors of 986 are 1, 2, 17, 29, 34, 58, 493, 986
The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165
The HCF of 986,165 is 1.
Lets's calculate GCF of 986,165
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 986,165 By Matching Biggest Common Factor Method
Now, list down the factors of 986
:1,2,17,29,34,58,493,986
Now, list down the factors of 165
:1,3,5,11,15,33,55,165
Greatest Common Factor
We found the factors 986,165 . The biggest common factor number is the GCF number.
So the greatest common factor 986,165 is 1.
Lets's calculate LCM of 37,219
Given numbers has no common factors except 1. So, there LCM is their product i.e 8103
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8103
Therefore, the GCF of Fractions 986/37,165/219 is 1/8103
Least Common Multiple of 37,219 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 37,219 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(37,219) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(37,219) x common factors =1 x 1 = 1
LCM(37,219) = ( 37 × 219 ) / 1
LCM(37,219) = 8103 / 1
LCM(37,219) = 8103
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FAQs on GCF of Fractions of 986/37, 165/219
1. What is the HCF of 986,165?
The HCF of 986,165 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 986/37, 165/219?
Answer: GCF of Numerators as per given numbers 986/37, 165/219 is
GCF of Numerators i.e. for 986,165 is 1
LCM of denominators i.e. for 37,219 is 8103.
Thus, GCF of Fractions is 1/8103.Finally, GCF of Fractions for 986/37, 165/219 is 1/8103.