GCF of 918/225, 1782/919
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 918/225, 1782/919 i.e 54/206775 easily. The following is the detailed procedure to determine the greatest common factor of fractions 918/225, 1782/919.
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 918/225,1782/919?
Given fractions are 918/225,1782/919
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 918/225,1782/919, numerators are 918,1782
Denominators are 225,919
The GCF of 918,1782 is 54 .
LCM of 225,919 is 206775.
The greatest common factor of 918/225,1782/919 = [GCF of 918,1782]/[LCM of 225,919]= 54/206775
Therefore, the GCF of 918/225,1782/919 is 54/206775.
To find the highest common factor of 918,1782, we have to find the factors of both numbers and list the highest common factor.
The factors of 918 are 1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 102, 153, 306, 459, 918
The factors of 1782 are 1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 54, 66, 81, 99, 162, 198, 297, 594, 891, 1782
The HCF of 918,1782 is 54.
Lets's calculate GCF of 918,1782
| 2 | 918, 1782 |
| 3 | 459, 891 |
| 3 | 153, 297 |
| 3 | 51, 99 |
| 17, 33 |
∴ So the GCF of the given numbers is 2 x 3 x 3 x 3 = 54
Greatest Common Factor of 918,1782 By Matching Biggest Common Factor Method
Now, list down the factors of 918
:1,2,3,6,9,17,18,27,34,51,54,102,153,306,459,918
Now, list down the factors of 1782
:1,2,3,6,9,11,18,22,27,33,54,66,81,99,162,198,297,594,891,1782
Greatest Common Factor
We found the factors 918,1782 . The biggest common factor number is the GCF number.
So the greatest common factor 918,1782 is 54.
Lets's calculate LCM of 225,919
Given numbers has no common factors except 1. So, there LCM is their product i.e 206775
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 54/206775
Therefore, the GCF of Fractions 918/225,1782/919 is 54/206775
Least Common Multiple of 225,919 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 225,919 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(225,919) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(225,919) x common factors =1 x 1 = 1
LCM(225,919) = ( 225 × 919 ) / 1
LCM(225,919) = 206775 / 1
LCM(225,919) = 206775
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FAQs on GCF of Fractions of 918/225, 1782/919
1. What is the HCF of 918,1782?
The HCF of 918,1782 is 54
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 918/225, 1782/919?
Answer: GCF of Numerators as per given numbers 918/225, 1782/919 is
GCF of Numerators i.e. for 918,1782 is 54
LCM of denominators i.e. for 225,919 is 206775.
Thus, GCF of Fractions is 54/206775.Finally, GCF of Fractions for 918/225, 1782/919 is 54/206775.