GCF of 420/398, 8309/228
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 420/398, 8309/228 i.e 7/45372 easily. The following is the detailed procedure to determine the greatest common factor of fractions 420/398, 8309/228.
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 420/398,8309/228?
Given fractions are 420/398,8309/228
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 420/398,8309/228, numerators are 420,8309
Denominators are 398,228
The GCF of 420,8309 is 7 .
LCM of 398,228 is 45372.
The greatest common factor of 420/398,8309/228 = [GCF of 420,8309]/[LCM of 398,228]= 7/45372
Therefore, the GCF of 420/398,8309/228 is 7/45372.
To find the highest common factor of 420,8309, we have to find the factors of both numbers and list the highest common factor.
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The factors of 8309 are 1, 7, 1187, 8309
The HCF of 420,8309 is 7.
Lets's calculate GCF of 420,8309
| 7 | 420, 8309 |
| 60, 1187 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 420,8309 By Matching Biggest Common Factor Method
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Now, list down the factors of 8309
:1,7,1187,8309
Greatest Common Factor
We found the factors 420,8309 . The biggest common factor number is the GCF number.
So the greatest common factor 420,8309 is 7.
Lets's calculate LCM of 398,228
| 2 | 398, 228 |
| 199, 114 |
∴ So the LCM of the given numbers is 2 x 199 x 114 = 45372
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/45372
Therefore, the GCF of Fractions 420/398,8309/228 is 7/45372
Least Common Multiple of 398,228 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 398,228 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(398,228) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(398,228) x common factors =2 x 1 = 2
LCM(398,228) = ( 398 × 228 ) / 2
LCM(398,228) = 90744 / 2
LCM(398,228) = 45372
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FAQs on GCF of Fractions of 420/398, 8309/228
1. What is the HCF of 420,8309?
The HCF of 420,8309 is 7
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 420/398, 8309/228?
Answer: GCF of Numerators as per given numbers 420/398, 8309/228 is
GCF of Numerators i.e. for 420,8309 is 7
LCM of denominators i.e. for 398,228 is 45372.
Thus, GCF of Fractions is 7/45372.Finally, GCF of Fractions for 420/398, 8309/228 is 7/45372.