GCF of 440/213, 320/588
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 440/213, 320/588 i.e 40/41748 easily. The following is the detailed procedure to determine the greatest common factor of fractions 440/213, 320/588.
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 440/213,320/588?
Given fractions are 440/213,320/588
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 440/213,320/588, numerators are 440,320
Denominators are 213,588
The GCF of 440,320 is 40 .
LCM of 213,588 is 41748.
The greatest common factor of 440/213,320/588 = [GCF of 440,320]/[LCM of 213,588]= 40/41748
Therefore, the GCF of 440/213,320/588 is 40/41748.
To find the highest common factor of 440,320, we have to find the factors of both numbers and list the highest common factor.
The factors of 440 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440
The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
The HCF of 440,320 is 40.
Lets's calculate GCF of 440,320
| 2 | 440, 320 |
| 2 | 220, 160 |
| 2 | 110, 80 |
| 5 | 55, 40 |
| 11, 8 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40
Greatest Common Factor of 440,320 By Matching Biggest Common Factor Method
Now, list down the factors of 440
:1,2,4,5,8,10,11,20,22,40,44,55,88,110,220,440
Now, list down the factors of 320
:1,2,4,5,8,10,16,20,32,40,64,80,160,320
Greatest Common Factor
We found the factors 440,320 . The biggest common factor number is the GCF number.
So the greatest common factor 440,320 is 40.
Lets's calculate LCM of 213,588
| 3 | 213, 588 |
| 71, 196 |
∴ So the LCM of the given numbers is 3 x 71 x 196 = 41748
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/41748
Therefore, the GCF of Fractions 440/213,320/588 is 40/41748
Least Common Multiple of 213,588 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 213,588 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(213,588) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(213,588) x common factors =3 x 1 = 3
LCM(213,588) = ( 213 × 588 ) / 3
LCM(213,588) = 125244 / 3
LCM(213,588) = 41748
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FAQs on GCF of Fractions of 440/213, 320/588
1. What is the HCF of 440,320?
The HCF of 440,320 is 40
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 440/213, 320/588?
Answer: GCF of Numerators as per given numbers 440/213, 320/588 is
GCF of Numerators i.e. for 440,320 is 40
LCM of denominators i.e. for 213,588 is 41748.
Thus, GCF of Fractions is 40/41748.Finally, GCF of Fractions for 440/213, 320/588 is 40/41748.