GCF of 326/413, 420/147
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 326/413, 420/147 i.e 2/8673 easily. The following is the detailed procedure to determine the greatest common factor of fractions 326/413, 420/147.
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 326/413,420/147?
Given fractions are 326/413,420/147
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 326/413,420/147, numerators are 326,420
Denominators are 413,147
The GCF of 326,420 is 2 .
LCM of 413,147 is 8673.
The greatest common factor of 326/413,420/147 = [GCF of 326,420]/[LCM of 413,147]= 2/8673
Therefore, the GCF of 326/413,420/147 is 2/8673.
To find the highest common factor of 326,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 326 are 1, 2, 163, 326
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 326,420 is 2.
Lets's calculate GCF of 326,420
| 2 | 326, 420 |
| 163, 210 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 326,420 By Matching Biggest Common Factor Method
Now, list down the factors of 326
:1,2,163,326
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 326,420 . The biggest common factor number is the GCF number.
So the greatest common factor 326,420 is 2.
Lets's calculate LCM of 413,147
| 7 | 413, 147 |
| 59, 21 |
∴ So the LCM of the given numbers is 7 x 59 x 21 = 8673
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/8673
Therefore, the GCF of Fractions 326/413,420/147 is 2/8673
Least Common Multiple of 413,147 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 413,147 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(413,147) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(413,147) x common factors =7 x 1 = 7
LCM(413,147) = ( 413 × 147 ) / 7
LCM(413,147) = 60711 / 7
LCM(413,147) = 8673
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FAQs on GCF of Fractions of 326/413, 420/147
1. What is the HCF of 326,420?
The HCF of 326,420 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 326/413, 420/147?
Answer: GCF of Numerators as per given numbers 326/413, 420/147 is
GCF of Numerators i.e. for 326,420 is 2
LCM of denominators i.e. for 413,147 is 8673.
Thus, GCF of Fractions is 2/8673.Finally, GCF of Fractions for 326/413, 420/147 is 2/8673.