GCF of 206/658, 489/218, 782/718
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 206/658, 489/218, 782/718 i.e 1/25748198 easily. The following is the detailed procedure to determine the greatest common factor of fractions 206/658, 489/218, 782/718.
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 206/658,489/218,782/718?
Given fractions are 206/658,489/218,782/718
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 206/658,489/218,782/718, numerators are 206,489,782
Denominators are 658,218,718
The GCF of 206,489,782 is 1 .
LCM of 658,218,718 is 25748198.
The greatest common factor of 206/658,489/218,782/718 = [GCF of 206,489,782]/[LCM of 658,218,718]= 1/25748198
Therefore, the GCF of 206/658,489/218,782/718 is 1/25748198.
To find the highest common factor of 206,489,782, we have to find the factors of both numbers and list the highest common factor.
The factors of 206 are 1, 2, 103, 206
The factors of 489 are 1, 3, 163, 489
The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782
The HCF of 206,489,782 is 1.
Lets's calculate GCF of 206,489,782
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 206,489,782 By Matching Biggest Common Factor Method
Now, list down the factors of 206
:1,2,103,206
Now, list down the factors of 489
:1,3,163,489
Now, list down the factors of 782
:1,2,17,23,34,46,391,782
Greatest Common Factor
We found the factors 206,489,782 . The biggest common factor number is the GCF number.
So the greatest common factor 206,489,782 is 1.
Lets's calculate LCM of 658,218,718
| 2 | 658, 218, 718 |
| 329, 109, 359 |
∴ So the LCM of the given numbers is 2 x 329 x 109 x 359 = 25748198
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/25748198
Therefore, the GCF of Fractions 206/658,489/218,782/718 is 1/25748198
Least Common Multiple of 658,218,718 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 658,218,718 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(658,218,718) = 2
common factors(in case of two or more numbers have common factors) = 2
GCF(658,218,718) x common factors =2 x 2 = 4
LCM(658,218,718) = ( 658 × 218 × 718 ) / 4
LCM(658,218,718) = 102992792 / 4
LCM(658,218,718) = 25748198
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FAQs on GCF of Fractions of 206/658, 489/218, 782/718
1. What is the HCF of 206,489,782?
The HCF of 206,489,782 is 1
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 206/658, 489/218, 782/718?
Answer: GCF of Numerators as per given numbers 206/658, 489/218, 782/718 is
GCF of Numerators i.e. for 206,489,782 is 1
LCM of denominators i.e. for 658,218,718 is 25748198.
Thus, GCF of Fractions is 1/25748198.Finally, GCF of Fractions for 206/658, 489/218, 782/718 is 1/25748198.