GCF of 4017/644, 6870/3114
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4017/644, 6870/3114 i.e 3/1002708 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4017/644, 6870/3114.
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 4017/644,6870/3114?
Given fractions are 4017/644,6870/3114
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 4017/644,6870/3114, numerators are 4017,6870
Denominators are 644,3114
The GCF of 4017,6870 is 3 .
LCM of 644,3114 is 1002708.
The greatest common factor of 4017/644,6870/3114 = [GCF of 4017,6870]/[LCM of 644,3114]= 3/1002708
Therefore, the GCF of 4017/644,6870/3114 is 3/1002708.
To find the highest common factor of 4017,6870, we have to find the factors of both numbers and list the highest common factor.
The factors of 4017 are 1, 3, 13, 39, 103, 309, 1339, 4017
The factors of 6870 are 1, 2, 3, 5, 6, 10, 15, 30, 229, 458, 687, 1145, 1374, 2290, 3435, 6870
The HCF of 4017,6870 is 3.
Lets's calculate GCF of 4017,6870
| 3 | 4017, 6870 |
| 1339, 2290 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 4017,6870 By Matching Biggest Common Factor Method
Now, list down the factors of 4017
:1,3,13,39,103,309,1339,4017
Now, list down the factors of 6870
:1,2,3,5,6,10,15,30,229,458,687,1145,1374,2290,3435,6870
Greatest Common Factor
We found the factors 4017,6870 . The biggest common factor number is the GCF number.
So the greatest common factor 4017,6870 is 3.
Lets's calculate LCM of 644,3114
| 2 | 644, 3114 |
| 322, 1557 |
∴ So the LCM of the given numbers is 2 x 322 x 1557 = 1002708
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1002708
Therefore, the GCF of Fractions 4017/644,6870/3114 is 3/1002708
Least Common Multiple of 644,3114 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 644,3114 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(644,3114) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(644,3114) x common factors =2 x 1 = 2
LCM(644,3114) = ( 644 × 3114 ) / 2
LCM(644,3114) = 2005416 / 2
LCM(644,3114) = 1002708
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FAQs on GCF of Fractions of 4017/644, 6870/3114
1. What is the HCF of 4017,6870?
The HCF of 4017,6870 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 4017/644, 6870/3114?
Answer: GCF of Numerators as per given numbers 4017/644, 6870/3114 is
GCF of Numerators i.e. for 4017,6870 is 3
LCM of denominators i.e. for 644,3114 is 1002708.
Thus, GCF of Fractions is 3/1002708.Finally, GCF of Fractions for 4017/644, 6870/3114 is 3/1002708.