GCF of 166/22, 415/578
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 166/22, 415/578 i.e 83/6358 easily. The following is the detailed procedure to determine the greatest common factor of fractions 166/22, 415/578.
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 166/22,415/578?
Given fractions are 166/22,415/578
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 166/22,415/578, numerators are 166,415
Denominators are 22,578
The GCF of 166,415 is 83 .
LCM of 22,578 is 6358.
The greatest common factor of 166/22,415/578 = [GCF of 166,415]/[LCM of 22,578]= 83/6358
Therefore, the GCF of 166/22,415/578 is 83/6358.
To find the highest common factor of 166,415, we have to find the factors of both numbers and list the highest common factor.
The factors of 166 are 1, 2, 83, 166
The factors of 415 are 1, 5, 83, 415
The HCF of 166,415 is 83.
Lets's calculate GCF of 166,415
| 83 | 166, 415 |
| 2, 5 |
∴ So the GCF of the given numbers is 83 = 83
Greatest Common Factor of 166,415 By Matching Biggest Common Factor Method
Now, list down the factors of 166
:1,2,83,166
Now, list down the factors of 415
:1,5,83,415
Greatest Common Factor
We found the factors 166,415 . The biggest common factor number is the GCF number.
So the greatest common factor 166,415 is 83.
Lets's calculate LCM of 22,578
| 2 | 22, 578 |
| 11, 289 |
∴ So the LCM of the given numbers is 2 x 11 x 289 = 6358
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 83/6358
Therefore, the GCF of Fractions 166/22,415/578 is 83/6358
Least Common Multiple of 22,578 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 22,578 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(22,578) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(22,578) x common factors =2 x 1 = 2
LCM(22,578) = ( 22 × 578 ) / 2
LCM(22,578) = 12716 / 2
LCM(22,578) = 6358
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FAQs on GCF of Fractions of 166/22, 415/578
1. What is the HCF of 166,415?
The HCF of 166,415 is 83
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 166/22, 415/578?
Answer: GCF of Numerators as per given numbers 166/22, 415/578 is
GCF of Numerators i.e. for 166,415 is 83
LCM of denominators i.e. for 22,578 is 6358.
Thus, GCF of Fractions is 83/6358.Finally, GCF of Fractions for 166/22, 415/578 is 83/6358.