GCF of 4214/970, 5234/105
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4214/970, 5234/105 i.e 2/20370 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4214/970, 5234/105.
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 4214/970,5234/105?
Given fractions are 4214/970,5234/105
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 4214/970,5234/105, numerators are 4214,5234
Denominators are 970,105
The GCF of 4214,5234 is 2 .
LCM of 970,105 is 20370.
The greatest common factor of 4214/970,5234/105 = [GCF of 4214,5234]/[LCM of 970,105]= 2/20370
Therefore, the GCF of 4214/970,5234/105 is 2/20370.
To find the highest common factor of 4214,5234, 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 5234 are 1, 2, 2617, 5234
The HCF of 4214,5234 is 2.
Lets's calculate GCF of 4214,5234
| 2 | 4214, 5234 |
| 2107, 2617 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 4214,5234 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 5234
:1,2,2617,5234
Greatest Common Factor
We found the factors 4214,5234 . The biggest common factor number is the GCF number.
So the greatest common factor 4214,5234 is 2.
Lets's calculate LCM of 970,105
| 5 | 970, 105 |
| 194, 21 |
∴ So the LCM of the given numbers is 5 x 194 x 21 = 20370
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/20370
Therefore, the GCF of Fractions 4214/970,5234/105 is 2/20370
Least Common Multiple of 970,105 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 970,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(970,105) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(970,105) x common factors =5 x 1 = 5
LCM(970,105) = ( 970 × 105 ) / 5
LCM(970,105) = 101850 / 5
LCM(970,105) = 20370
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FAQs on GCF of Fractions of 4214/970, 5234/105
1. What is the HCF of 4214,5234?
The HCF of 4214,5234 is 2
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 4214/970, 5234/105?
Answer: GCF of Numerators as per given numbers 4214/970, 5234/105 is
GCF of Numerators i.e. for 4214,5234 is 2
LCM of denominators i.e. for 970,105 is 20370.
Thus, GCF of Fractions is 2/20370.Finally, GCF of Fractions for 4214/970, 5234/105 is 2/20370.