GCF of 4214/226, 8582/1306
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4214/226, 8582/1306 i.e 14/147578 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4214/226, 8582/1306.
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 4214/226,8582/1306?
Given fractions are 4214/226,8582/1306
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 4214/226,8582/1306, numerators are 4214,8582
Denominators are 226,1306
The GCF of 4214,8582 is 14 .
LCM of 226,1306 is 147578.
The greatest common factor of 4214/226,8582/1306 = [GCF of 4214,8582]/[LCM of 226,1306]= 14/147578
Therefore, the GCF of 4214/226,8582/1306 is 14/147578.
To find the highest common factor of 4214,8582, we have to find the factors of both numbers and list the highest common factor.
The factors of 4214 are 1, 2, 7, 14, 43, 49, 86, 98, 301, 602, 2107, 4214
The factors of 8582 are 1, 2, 7, 14, 613, 1226, 4291, 8582
The HCF of 4214,8582 is 14.
Lets's calculate GCF of 4214,8582
| 2 | 4214, 8582 |
| 7 | 2107, 4291 |
| 301, 613 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 4214,8582 By Matching Biggest Common Factor Method
Now, list down the factors of 4214
:1,2,7,14,43,49,86,98,301,602,2107,4214
Now, list down the factors of 8582
:1,2,7,14,613,1226,4291,8582
Greatest Common Factor
We found the factors 4214,8582 . The biggest common factor number is the GCF number.
So the greatest common factor 4214,8582 is 14.
Lets's calculate LCM of 226,1306
| 2 | 226, 1306 |
| 113, 653 |
∴ So the LCM of the given numbers is 2 x 113 x 653 = 147578
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/147578
Therefore, the GCF of Fractions 4214/226,8582/1306 is 14/147578
Least Common Multiple of 226,1306 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 226,1306 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(226,1306) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(226,1306) x common factors =2 x 1 = 2
LCM(226,1306) = ( 226 × 1306 ) / 2
LCM(226,1306) = 295156 / 2
LCM(226,1306) = 147578
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FAQs on GCF of Fractions of 4214/226, 8582/1306
1. What is the HCF of 4214,8582?
The HCF of 4214,8582 is 14
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 4214/226, 8582/1306?
Answer: GCF of Numerators as per given numbers 4214/226, 8582/1306 is
GCF of Numerators i.e. for 4214,8582 is 14
LCM of denominators i.e. for 226,1306 is 147578.
Thus, GCF of Fractions is 14/147578.Finally, GCF of Fractions for 4214/226, 8582/1306 is 14/147578.