GCF of 406/205, 480/235
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 406/205, 480/235 i.e 2/9635 easily. The following is the detailed procedure to determine the greatest common factor of fractions 406/205, 480/235.
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 406/205,480/235?
Given fractions are 406/205,480/235
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 406/205,480/235, numerators are 406,480
Denominators are 205,235
The GCF of 406,480 is 2 .
LCM of 205,235 is 9635.
The greatest common factor of 406/205,480/235 = [GCF of 406,480]/[LCM of 205,235]= 2/9635
Therefore, the GCF of 406/205,480/235 is 2/9635.
To find the highest common factor of 406,480, we have to find the factors of both numbers and list the highest common factor.
The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406
The factors of 480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480
The HCF of 406,480 is 2.
Lets's calculate GCF of 406,480
| 2 | 406, 480 |
| 203, 240 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 406,480 By Matching Biggest Common Factor Method
Now, list down the factors of 406
:1,2,7,14,29,58,203,406
Now, list down the factors of 480
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,80,96,120,160,240,480
Greatest Common Factor
We found the factors 406,480 . The biggest common factor number is the GCF number.
So the greatest common factor 406,480 is 2.
Lets's calculate LCM of 205,235
| 5 | 205, 235 |
| 41, 47 |
∴ So the LCM of the given numbers is 5 x 41 x 47 = 9635
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/9635
Therefore, the GCF of Fractions 406/205,480/235 is 2/9635
Least Common Multiple of 205,235 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 205,235 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,235) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(205,235) x common factors =5 x 1 = 5
LCM(205,235) = ( 205 × 235 ) / 5
LCM(205,235) = 48175 / 5
LCM(205,235) = 9635
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FAQs on GCF of Fractions of 406/205, 480/235
1. What is the HCF of 406,480?
The HCF of 406,480 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 406/205, 480/235?
Answer: GCF of Numerators as per given numbers 406/205, 480/235 is
GCF of Numerators i.e. for 406,480 is 2
LCM of denominators i.e. for 205,235 is 9635.
Thus, GCF of Fractions is 2/9635.Finally, GCF of Fractions for 406/205, 480/235 is 2/9635.