GCF of 8730/106, 4149/7014
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8730/106, 4149/7014 i.e 9/371742 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8730/106, 4149/7014.
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 8730/106,4149/7014?
Given fractions are 8730/106,4149/7014
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 8730/106,4149/7014, numerators are 8730,4149
Denominators are 106,7014
The GCF of 8730,4149 is 9 .
LCM of 106,7014 is 371742.
The greatest common factor of 8730/106,4149/7014 = [GCF of 8730,4149]/[LCM of 106,7014]= 9/371742
Therefore, the GCF of 8730/106,4149/7014 is 9/371742.
To find the highest common factor of 8730,4149, we have to find the factors of both numbers and list the highest common factor.
The factors of 8730 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 97, 194, 291, 485, 582, 873, 970, 1455, 1746, 2910, 4365, 8730
The factors of 4149 are 1, 3, 9, 461, 1383, 4149
The HCF of 8730,4149 is 9.
Lets's calculate GCF of 8730,4149
| 3 | 8730, 4149 |
| 3 | 2910, 1383 |
| 970, 461 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 8730,4149 By Matching Biggest Common Factor Method
Now, list down the factors of 8730
:1,2,3,5,6,9,10,15,18,30,45,90,97,194,291,485,582,873,970,1455,1746,2910,4365,8730
Now, list down the factors of 4149
:1,3,9,461,1383,4149
Greatest Common Factor
We found the factors 8730,4149 . The biggest common factor number is the GCF number.
So the greatest common factor 8730,4149 is 9.
Lets's calculate LCM of 106,7014
| 2 | 106, 7014 |
| 53, 3507 |
∴ So the LCM of the given numbers is 2 x 53 x 3507 = 371742
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/371742
Therefore, the GCF of Fractions 8730/106,4149/7014 is 9/371742
Least Common Multiple of 106,7014 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 106,7014 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(106,7014) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(106,7014) x common factors =2 x 1 = 2
LCM(106,7014) = ( 106 × 7014 ) / 2
LCM(106,7014) = 743484 / 2
LCM(106,7014) = 371742
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FAQs on GCF of Fractions of 8730/106, 4149/7014
1. What is the HCF of 8730,4149?
The HCF of 8730,4149 is 9
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 8730/106, 4149/7014?
Answer: GCF of Numerators as per given numbers 8730/106, 4149/7014 is
GCF of Numerators i.e. for 8730,4149 is 9
LCM of denominators i.e. for 106,7014 is 371742.
Thus, GCF of Fractions is 9/371742.Finally, GCF of Fractions for 8730/106, 4149/7014 is 9/371742.