GCF of 426/409, 420/631
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 426/409, 420/631 i.e 6/258079 easily. The following is the detailed procedure to determine the greatest common factor of fractions 426/409, 420/631.
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 426/409,420/631?
Given fractions are 426/409,420/631
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 426/409,420/631, numerators are 426,420
Denominators are 409,631
The GCF of 426,420 is 6 .
LCM of 409,631 is 258079.
The greatest common factor of 426/409,420/631 = [GCF of 426,420]/[LCM of 409,631]= 6/258079
Therefore, the GCF of 426/409,420/631 is 6/258079.
To find the highest common factor of 426,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 426 are 1, 2, 3, 6, 71, 142, 213, 426
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 HCF of 426,420 is 6.
Lets's calculate GCF of 426,420
| 2 | 426, 420 |
| 3 | 213, 210 |
| 71, 70 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 426,420 By Matching Biggest Common Factor Method
Now, list down the factors of 426
:1,2,3,6,71,142,213,426
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
Greatest Common Factor
We found the factors 426,420 . The biggest common factor number is the GCF number.
So the greatest common factor 426,420 is 6.
Lets's calculate LCM of 409,631
Given numbers has no common factors except 1. So, there LCM is their product i.e 258079
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/258079
Therefore, the GCF of Fractions 426/409,420/631 is 6/258079
Least Common Multiple of 409,631 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 409,631 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(409,631) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(409,631) x common factors =1 x 1 = 1
LCM(409,631) = ( 409 × 631 ) / 1
LCM(409,631) = 258079 / 1
LCM(409,631) = 258079
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FAQs on GCF of Fractions of 426/409, 420/631
1. What is the HCF of 426,420?
The HCF of 426,420 is 6
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 426/409, 420/631?
Answer: GCF of Numerators as per given numbers 426/409, 420/631 is
GCF of Numerators i.e. for 426,420 is 6
LCM of denominators i.e. for 409,631 is 258079.
Thus, GCF of Fractions is 6/258079.Finally, GCF of Fractions for 426/409, 420/631 is 6/258079.