GCF of 460/819, 640/224
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 460/819, 640/224 i.e 20/26208 easily. The following is the detailed procedure to determine the greatest common factor of fractions 460/819, 640/224.
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 460/819,640/224?
Given fractions are 460/819,640/224
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 460/819,640/224, numerators are 460,640
Denominators are 819,224
The GCF of 460,640 is 20 .
LCM of 819,224 is 26208.
The greatest common factor of 460/819,640/224 = [GCF of 460,640]/[LCM of 819,224]= 20/26208
Therefore, the GCF of 460/819,640/224 is 20/26208.
To find the highest common factor of 460,640, we have to find the factors of both numbers and list the highest common factor.
The factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
The factors of 640 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 320, 640
The HCF of 460,640 is 20.
Lets's calculate GCF of 460,640
| 2 | 460, 640 |
| 2 | 230, 320 |
| 5 | 115, 160 |
| 23, 32 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 460,640 By Matching Biggest Common Factor Method
Now, list down the factors of 460
:1,2,4,5,10,20,23,46,92,115,230,460
Now, list down the factors of 640
:1,2,4,5,8,10,16,20,32,40,64,80,128,160,320,640
Greatest Common Factor
We found the factors 460,640 . The biggest common factor number is the GCF number.
So the greatest common factor 460,640 is 20.
Lets's calculate LCM of 819,224
| 7 | 819, 224 |
| 117, 32 |
∴ So the LCM of the given numbers is 7 x 117 x 32 = 26208
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/26208
Therefore, the GCF of Fractions 460/819,640/224 is 20/26208
Least Common Multiple of 819,224 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 819,224 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(819,224) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(819,224) x common factors =7 x 1 = 7
LCM(819,224) = ( 819 × 224 ) / 7
LCM(819,224) = 183456 / 7
LCM(819,224) = 26208
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 460/819, 640/224
1. What is the HCF of 460,640?
The HCF of 460,640 is 20
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 460/819, 640/224?
Answer: GCF of Numerators as per given numbers 460/819, 640/224 is
GCF of Numerators i.e. for 460,640 is 20
LCM of denominators i.e. for 819,224 is 26208.
Thus, GCF of Fractions is 20/26208.Finally, GCF of Fractions for 460/819, 640/224 is 20/26208.