GCF of 5214/218, 8019/686
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5214/218, 8019/686 i.e 33/74774 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5214/218, 8019/686.
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 5214/218,8019/686?
Given fractions are 5214/218,8019/686
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 5214/218,8019/686, numerators are 5214,8019
Denominators are 218,686
The GCF of 5214,8019 is 33 .
LCM of 218,686 is 74774.
The greatest common factor of 5214/218,8019/686 = [GCF of 5214,8019]/[LCM of 218,686]= 33/74774
Therefore, the GCF of 5214/218,8019/686 is 33/74774.
To find the highest common factor of 5214,8019, we have to find the factors of both numbers and list the highest common factor.
The factors of 5214 are 1, 2, 3, 6, 11, 22, 33, 66, 79, 158, 237, 474, 869, 1738, 2607, 5214
The factors of 8019 are 1, 3, 9, 11, 27, 33, 81, 99, 243, 297, 729, 891, 2673, 8019
The HCF of 5214,8019 is 33.
Lets's calculate GCF of 5214,8019
| 3 | 5214, 8019 |
| 11 | 1738, 2673 |
| 158, 243 |
∴ So the GCF of the given numbers is 3 x 11 = 33
Greatest Common Factor of 5214,8019 By Matching Biggest Common Factor Method
Now, list down the factors of 5214
:1,2,3,6,11,22,33,66,79,158,237,474,869,1738,2607,5214
Now, list down the factors of 8019
:1,3,9,11,27,33,81,99,243,297,729,891,2673,8019
Greatest Common Factor
We found the factors 5214,8019 . The biggest common factor number is the GCF number.
So the greatest common factor 5214,8019 is 33.
Lets's calculate LCM of 218,686
| 2 | 218, 686 |
| 109, 343 |
∴ So the LCM of the given numbers is 2 x 109 x 343 = 74774
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 33/74774
Therefore, the GCF of Fractions 5214/218,8019/686 is 33/74774
Least Common Multiple of 218,686 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 218,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(218,686) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(218,686) x common factors =2 x 1 = 2
LCM(218,686) = ( 218 × 686 ) / 2
LCM(218,686) = 149548 / 2
LCM(218,686) = 74774
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FAQs on GCF of Fractions of 5214/218, 8019/686
1. What is the HCF of 5214,8019?
The HCF of 5214,8019 is 33
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 5214/218, 8019/686?
Answer: GCF of Numerators as per given numbers 5214/218, 8019/686 is
GCF of Numerators i.e. for 5214,8019 is 33
LCM of denominators i.e. for 218,686 is 74774.
Thus, GCF of Fractions is 33/74774.Finally, GCF of Fractions for 5214/218, 8019/686 is 33/74774.