GCF of 8378/228, 8463/2214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8378/228, 8463/2214 i.e 1/84132 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8378/228, 8463/2214.
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 8378/228,8463/2214?
Given fractions are 8378/228,8463/2214
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 8378/228,8463/2214, numerators are 8378,8463
Denominators are 228,2214
The GCF of 8378,8463 is 1 .
LCM of 228,2214 is 84132.
The greatest common factor of 8378/228,8463/2214 = [GCF of 8378,8463]/[LCM of 228,2214]= 1/84132
Therefore, the GCF of 8378/228,8463/2214 is 1/84132.
To find the highest common factor of 8378,8463, we have to find the factors of both numbers and list the highest common factor.
The factors of 8378 are 1, 2, 59, 71, 118, 142, 4189, 8378
The factors of 8463 are 1, 3, 7, 13, 21, 31, 39, 91, 93, 217, 273, 403, 651, 1209, 2821, 8463
The HCF of 8378,8463 is 1.
Lets's calculate GCF of 8378,8463
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 8378,8463 By Matching Biggest Common Factor Method
Now, list down the factors of 8378
:1,2,59,71,118,142,4189,8378
Now, list down the factors of 8463
:1,3,7,13,21,31,39,91,93,217,273,403,651,1209,2821,8463
Greatest Common Factor
We found the factors 8378,8463 . The biggest common factor number is the GCF number.
So the greatest common factor 8378,8463 is 1.
Lets's calculate LCM of 228,2214
| 2 | 228, 2214 |
| 3 | 114, 1107 |
| 38, 369 |
∴ So the LCM of the given numbers is 2 x 3 x 38 x 369 = 84132
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/84132
Therefore, the GCF of Fractions 8378/228,8463/2214 is 1/84132
Least Common Multiple of 228,2214 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 228,2214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(228,2214) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(228,2214) x common factors =6 x 1 = 6
LCM(228,2214) = ( 228 × 2214 ) / 6
LCM(228,2214) = 504792 / 6
LCM(228,2214) = 84132
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FAQs on GCF of Fractions of 8378/228, 8463/2214
1. What is the HCF of 8378,8463?
The HCF of 8378,8463 is 1
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 8378/228, 8463/2214?
Answer: GCF of Numerators as per given numbers 8378/228, 8463/2214 is
GCF of Numerators i.e. for 8378,8463 is 1
LCM of denominators i.e. for 228,2214 is 84132.
Thus, GCF of Fractions is 1/84132.Finally, GCF of Fractions for 8378/228, 8463/2214 is 1/84132.