GCF of 400/214, 3430/4205
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 400/214, 3430/4205 i.e 10/899870 easily. The following is the detailed procedure to determine the greatest common factor of fractions 400/214, 3430/4205.
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 400/214,3430/4205?
Given fractions are 400/214,3430/4205
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 400/214,3430/4205, numerators are 400,3430
Denominators are 214,4205
The GCF of 400,3430 is 10 .
LCM of 214,4205 is 899870.
The greatest common factor of 400/214,3430/4205 = [GCF of 400,3430]/[LCM of 214,4205]= 10/899870
Therefore, the GCF of 400/214,3430/4205 is 10/899870.
To find the highest common factor of 400,3430, we have to find the factors of both numbers and list the highest common factor.
The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
The factors of 3430 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 343, 490, 686, 1715, 3430
The HCF of 400,3430 is 10.
Lets's calculate GCF of 400,3430
| 2 | 400, 3430 |
| 5 | 200, 1715 |
| 40, 343 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 400,3430 By Matching Biggest Common Factor Method
Now, list down the factors of 400
:1,2,4,5,8,10,16,20,25,40,50,80,100,200,400
Now, list down the factors of 3430
:1,2,5,7,10,14,35,49,70,98,245,343,490,686,1715,3430
Greatest Common Factor
We found the factors 400,3430 . The biggest common factor number is the GCF number.
So the greatest common factor 400,3430 is 10.
Lets's calculate LCM of 214,4205
Given numbers has no common factors except 1. So, there LCM is their product i.e 899870
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/899870
Therefore, the GCF of Fractions 400/214,3430/4205 is 10/899870
Least Common Multiple of 214,4205 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 214,4205 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(214,4205) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(214,4205) x common factors =1 x 1 = 1
LCM(214,4205) = ( 214 × 4205 ) / 1
LCM(214,4205) = 899870 / 1
LCM(214,4205) = 899870
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FAQs on GCF of Fractions of 400/214, 3430/4205
1. What is the HCF of 400,3430?
The HCF of 400,3430 is 10
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 400/214, 3430/4205?
Answer: GCF of Numerators as per given numbers 400/214, 3430/4205 is
GCF of Numerators i.e. for 400,3430 is 10
LCM of denominators i.e. for 214,4205 is 899870.
Thus, GCF of Fractions is 10/899870.Finally, GCF of Fractions for 400/214, 3430/4205 is 10/899870.