GCF of 3678/514, 5214/674
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3678/514, 5214/674 i.e 6/173218 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3678/514, 5214/674.
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 3678/514,5214/674?
Given fractions are 3678/514,5214/674
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 3678/514,5214/674, numerators are 3678,5214
Denominators are 514,674
The GCF of 3678,5214 is 6 .
LCM of 514,674 is 173218.
The greatest common factor of 3678/514,5214/674 = [GCF of 3678,5214]/[LCM of 514,674]= 6/173218
Therefore, the GCF of 3678/514,5214/674 is 6/173218.
To find the highest common factor of 3678,5214, we have to find the factors of both numbers and list the highest common factor.
The factors of 3678 are 1, 2, 3, 6, 613, 1226, 1839, 3678
The factors of 5214 are 1, 2, 3, 6, 11, 22, 33, 66, 79, 158, 237, 474, 869, 1738, 2607, 5214
The HCF of 3678,5214 is 6.
Lets's calculate GCF of 3678,5214
| 2 | 3678, 5214 |
| 3 | 1839, 2607 |
| 613, 869 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 3678,5214 By Matching Biggest Common Factor Method
Now, list down the factors of 3678
:1,2,3,6,613,1226,1839,3678
Now, list down the factors of 5214
:1,2,3,6,11,22,33,66,79,158,237,474,869,1738,2607,5214
Greatest Common Factor
We found the factors 3678,5214 . The biggest common factor number is the GCF number.
So the greatest common factor 3678,5214 is 6.
Lets's calculate LCM of 514,674
| 2 | 514, 674 |
| 257, 337 |
∴ So the LCM of the given numbers is 2 x 257 x 337 = 173218
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/173218
Therefore, the GCF of Fractions 3678/514,5214/674 is 6/173218
Least Common Multiple of 514,674 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 514,674 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(514,674) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(514,674) x common factors =2 x 1 = 2
LCM(514,674) = ( 514 × 674 ) / 2
LCM(514,674) = 346436 / 2
LCM(514,674) = 173218
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FAQs on GCF of Fractions of 3678/514, 5214/674
1. What is the HCF of 3678,5214?
The HCF of 3678,5214 is 6
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 3678/514, 5214/674?
Answer: GCF of Numerators as per given numbers 3678/514, 5214/674 is
GCF of Numerators i.e. for 3678,5214 is 6
LCM of denominators i.e. for 514,674 is 173218.
Thus, GCF of Fractions is 6/173218.Finally, GCF of Fractions for 3678/514, 5214/674 is 6/173218.