GCF of 90/49, 214/17, 256/489
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 90/49, 214/17, 256/489 i.e 2/407337 easily. The following is the detailed procedure to determine the greatest common factor of fractions 90/49, 214/17, 256/489.
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 90/49,214/17,256/489?
Given fractions are 90/49,214/17,256/489
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 90/49,214/17,256/489, numerators are 90,214,256
Denominators are 49,17,489
The GCF of 90,214,256 is 2 .
LCM of 49,17,489 is 407337.
The greatest common factor of 90/49,214/17,256/489 = [GCF of 90,214,256]/[LCM of 49,17,489]= 2/407337
Therefore, the GCF of 90/49,214/17,256/489 is 2/407337.
To find the highest common factor of 90,214,256, we have to find the factors of both numbers and list the highest common factor.
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The factors of 214 are 1, 2, 107, 214
The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256
The HCF of 90,214,256 is 2.
Lets's calculate GCF of 90,214,256
| 2 | 90, 214, 256 |
| 45, 107, 128 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 90,214,256 By Matching Biggest Common Factor Method
Now, list down the factors of 90
:1,2,3,5,6,9,10,15,18,30,45,90
Now, list down the factors of 214
:1,2,107,214
Now, list down the factors of 256
:1,2,4,8,16,32,64,128,256
Greatest Common Factor
We found the factors 90,214,256 . The biggest common factor number is the GCF number.
So the greatest common factor 90,214,256 is 2.
Lets's calculate LCM of 49,17,489
Given numbers has no common factors except 1. So, there LCM is their product i.e 407337
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/407337
Therefore, the GCF of Fractions 90/49,214/17,256/489 is 2/407337
Least Common Multiple of 49,17,489 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 49,17,489 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,17,489) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(49,17,489) x common factors =1 x 1 = 1
LCM(49,17,489) = ( 49 × 17 × 489 ) / 1
LCM(49,17,489) = 407337 / 1
LCM(49,17,489) = 407337
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FAQs on GCF of Fractions of 90/49, 214/17, 256/489
1. What is the HCF of 90,214,256?
The HCF of 90,214,256 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 90/49, 214/17, 256/489?
Answer: GCF of Numerators as per given numbers 90/49, 214/17, 256/489 is
GCF of Numerators i.e. for 90,214,256 is 2
LCM of denominators i.e. for 49,17,489 is 407337.
Thus, GCF of Fractions is 2/407337.Finally, GCF of Fractions for 90/49, 214/17, 256/489 is 2/407337.