GCF of 855/72, 177/414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 855/72, 177/414 i.e 3/1656 easily. The following is the detailed procedure to determine the greatest common factor of fractions 855/72, 177/414.
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 855/72,177/414?
Given fractions are 855/72,177/414
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 855/72,177/414, numerators are 855,177
Denominators are 72,414
The GCF of 855,177 is 3 .
LCM of 72,414 is 1656.
The greatest common factor of 855/72,177/414 = [GCF of 855,177]/[LCM of 72,414]= 3/1656
Therefore, the GCF of 855/72,177/414 is 3/1656.
To find the highest common factor of 855,177, we have to find the factors of both numbers and list the highest common factor.
The factors of 855 are 1, 3, 5, 9, 15, 19, 45, 57, 95, 171, 285, 855
The factors of 177 are 1, 3, 59, 177
The HCF of 855,177 is 3.
Lets's calculate GCF of 855,177
| 3 | 855, 177 |
| 285, 59 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 855,177 By Matching Biggest Common Factor Method
Now, list down the factors of 855
:1,3,5,9,15,19,45,57,95,171,285,855
Now, list down the factors of 177
:1,3,59,177
Greatest Common Factor
We found the factors 855,177 . The biggest common factor number is the GCF number.
So the greatest common factor 855,177 is 3.
Lets's calculate LCM of 72,414
| 2 | 72, 414 |
| 3 | 36, 207 |
| 3 | 12, 69 |
| 4, 23 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 4 x 23 = 1656
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1656
Therefore, the GCF of Fractions 855/72,177/414 is 3/1656
Least Common Multiple of 72,414 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 72,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(72,414) = 18
common factors(in case of two or more numbers have common factors) = 1
GCF(72,414) x common factors =18 x 1 = 18
LCM(72,414) = ( 72 × 414 ) / 18
LCM(72,414) = 29808 / 18
LCM(72,414) = 1656
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FAQs on GCF of Fractions of 855/72, 177/414
1. What is the HCF of 855,177?
The HCF of 855,177 is 3
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 855/72, 177/414?
Answer: GCF of Numerators as per given numbers 855/72, 177/414 is
GCF of Numerators i.e. for 855,177 is 3
LCM of denominators i.e. for 72,414 is 1656.
Thus, GCF of Fractions is 3/1656.Finally, GCF of Fractions for 855/72, 177/414 is 3/1656.