GCF of 660/31, 165/638
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 660/31, 165/638 i.e 165/19778 easily. The following is the detailed procedure to determine the greatest common factor of fractions 660/31, 165/638.
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 660/31,165/638?
Given fractions are 660/31,165/638
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 660/31,165/638, numerators are 660,165
Denominators are 31,638
The GCF of 660,165 is 165 .
LCM of 31,638 is 19778.
The greatest common factor of 660/31,165/638 = [GCF of 660,165]/[LCM of 31,638]= 165/19778
Therefore, the GCF of 660/31,165/638 is 165/19778.
To find the highest common factor of 660,165, we have to find the factors of both numbers and list the highest common factor.
The factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660
The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165
The HCF of 660,165 is 165.
Lets's calculate GCF of 660,165
| 3 | 660, 165 |
| 5 | 220, 55 |
| 11 | 44, 11 |
| 4, 1 |
∴ So the GCF of the given numbers is 3 x 5 x 11 = 165
Greatest Common Factor of 660,165 By Matching Biggest Common Factor Method
Now, list down the factors of 660
:1,2,3,4,5,6,10,11,12,15,20,22,30,33,44,55,60,66,110,132,165,220,330,660
Now, list down the factors of 165
:1,3,5,11,15,33,55,165
Greatest Common Factor
We found the factors 660,165 . The biggest common factor number is the GCF number.
So the greatest common factor 660,165 is 165.
Lets's calculate LCM of 31,638
Given numbers has no common factors except 1. So, there LCM is their product i.e 19778
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 165/19778
Therefore, the GCF of Fractions 660/31,165/638 is 165/19778
Least Common Multiple of 31,638 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 31,638 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,638) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,638) x common factors =1 x 1 = 1
LCM(31,638) = ( 31 × 638 ) / 1
LCM(31,638) = 19778 / 1
LCM(31,638) = 19778
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FAQs on GCF of Fractions of 660/31, 165/638
1. What is the HCF of 660,165?
The HCF of 660,165 is 165
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 660/31, 165/638?
Answer: GCF of Numerators as per given numbers 660/31, 165/638 is
GCF of Numerators i.e. for 660,165 is 165
LCM of denominators i.e. for 31,638 is 19778.
Thus, GCF of Fractions is 165/19778.Finally, GCF of Fractions for 660/31, 165/638 is 165/19778.