GCF of 805/218, 1242/504
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 805/218, 1242/504 i.e 23/54936 easily. The following is the detailed procedure to determine the greatest common factor of fractions 805/218, 1242/504.
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 805/218,1242/504?
Given fractions are 805/218,1242/504
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 805/218,1242/504, numerators are 805,1242
Denominators are 218,504
The GCF of 805,1242 is 23 .
LCM of 218,504 is 54936.
The greatest common factor of 805/218,1242/504 = [GCF of 805,1242]/[LCM of 218,504]= 23/54936
Therefore, the GCF of 805/218,1242/504 is 23/54936.
To find the highest common factor of 805,1242, we have to find the factors of both numbers and list the highest common factor.
The factors of 805 are 1, 5, 7, 23, 35, 115, 161, 805
The factors of 1242 are 1, 2, 3, 6, 9, 18, 23, 27, 46, 54, 69, 138, 207, 414, 621, 1242
The HCF of 805,1242 is 23.
Lets's calculate GCF of 805,1242
| 23 | 805, 1242 |
| 35, 54 |
∴ So the GCF of the given numbers is 23 = 23
Greatest Common Factor of 805,1242 By Matching Biggest Common Factor Method
Now, list down the factors of 805
:1,5,7,23,35,115,161,805
Now, list down the factors of 1242
:1,2,3,6,9,18,23,27,46,54,69,138,207,414,621,1242
Greatest Common Factor
We found the factors 805,1242 . The biggest common factor number is the GCF number.
So the greatest common factor 805,1242 is 23.
Lets's calculate LCM of 218,504
| 2 | 218, 504 |
| 109, 252 |
∴ So the LCM of the given numbers is 2 x 109 x 252 = 54936
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/54936
Therefore, the GCF of Fractions 805/218,1242/504 is 23/54936
Least Common Multiple of 218,504 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 218,504 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(218,504) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(218,504) x common factors =2 x 1 = 2
LCM(218,504) = ( 218 × 504 ) / 2
LCM(218,504) = 109872 / 2
LCM(218,504) = 54936
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FAQs on GCF of Fractions of 805/218, 1242/504
1. What is the HCF of 805,1242?
The HCF of 805,1242 is 23
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 805/218, 1242/504?
Answer: GCF of Numerators as per given numbers 805/218, 1242/504 is
GCF of Numerators i.e. for 805,1242 is 23
LCM of denominators i.e. for 218,504 is 54936.
Thus, GCF of Fractions is 23/54936.Finally, GCF of Fractions for 805/218, 1242/504 is 23/54936.