GCF of 640/414, 584/775, 542/852
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 640/414, 584/775, 542/852 i.e 2/45560700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 640/414, 584/775, 542/852.
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 640/414,584/775,542/852?
Given fractions are 640/414,584/775,542/852
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 640/414,584/775,542/852, numerators are 640,584,542
Denominators are 414,775,852
The GCF of 640,584,542 is 2 .
LCM of 414,775,852 is 45560700.
The greatest common factor of 640/414,584/775,542/852 = [GCF of 640,584,542]/[LCM of 414,775,852]= 2/45560700
Therefore, the GCF of 640/414,584/775,542/852 is 2/45560700.
To find the highest common factor of 640,584,542, we have to find the factors of both numbers and list the highest common factor.
The factors of 640 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 320, 640
The factors of 584 are 1, 2, 4, 8, 73, 146, 292, 584
The factors of 542 are 1, 2, 271, 542
The HCF of 640,584,542 is 2.
Lets's calculate GCF of 640,584,542
| 2 | 640, 584, 542 |
| 320, 292, 271 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 640,584,542 By Matching Biggest Common Factor Method
Now, list down the factors of 640
:1,2,4,5,8,10,16,20,32,40,64,80,128,160,320,640
Now, list down the factors of 584
:1,2,4,8,73,146,292,584
Now, list down the factors of 542
:1,2,271,542
Greatest Common Factor
We found the factors 640,584,542 . The biggest common factor number is the GCF number.
So the greatest common factor 640,584,542 is 2.
Lets's calculate LCM of 414,775,852
| 2 | 414, 775, 852 |
| 3 | 207, 775, 426 |
| 69, 775, 142 |
∴ So the LCM of the given numbers is 2 x 3 x 69 x 775 x 142 = 45560700
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/45560700
Therefore, the GCF of Fractions 640/414,584/775,542/852 is 2/45560700
Least Common Multiple of 414,775,852 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 414,775,852 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,775,852) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(414,775,852) x common factors =1 x 6 = 6
LCM(414,775,852) = ( 414 × 775 × 852 ) / 6
LCM(414,775,852) = 273364200 / 6
LCM(414,775,852) = 45560700
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 640/414, 584/775, 542/852
1. What is the HCF of 640,584,542?
The HCF of 640,584,542 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 640/414, 584/775, 542/852?
Answer: GCF of Numerators as per given numbers 640/414, 584/775, 542/852 is
GCF of Numerators i.e. for 640,584,542 is 2
LCM of denominators i.e. for 414,775,852 is 45560700.
Thus, GCF of Fractions is 2/45560700.Finally, GCF of Fractions for 640/414, 584/775, 542/852 is 2/45560700.