Use our free GCF of Fractions Calculator tool to compute the GCF of 489/546, 800/714 i.e 1/9282 easily. The following is the detailed procedure to determine the greatest common factor of fractions 489/546, 800/714.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 489/546,800/714
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 489/546,800/714, numerators are 489,800
Denominators are 546,714
The GCF of 489,800 is 1 .
LCM of 546,714 is 9282.
The greatest common factor of 489/546,800/714 = [GCF of 489,800]/[LCM of 546,714]= 1/9282
Therefore, the GCF of 489/546,800/714 is 1/9282.
To find the highest common factor of 489,800, we have to find the factors of both numbers and list the highest common factor.
The factors of 489 are 1, 3, 163, 489
The factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800
The HCF of 489,800 is 1.
Lets's calculate GCF of 489,800
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 489
:1,3,163,489
Now, list down the factors of 800
:1,2,4,5,8,10,16,20,25,32,40,50,80,100,160,200,400,800
Greatest Common Factor
We found the factors 489,800 . The biggest common factor number is the GCF number.
So the greatest common factor 489,800 is 1.
Lets's calculate LCM of 546,714
2 | 546, 714 |
3 | 273, 357 |
7 | 91, 119 |
13, 17 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 13 x 17 = 9282
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9282
Therefore, the GCF of Fractions 489/546,800/714 is 1/9282
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 546,714 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(546,714) = 42
common factors(in case of two or more numbers have common factors) = 1
GCF(546,714) x common factors =42 x 1 = 42
LCM(546,714) = ( 546 × 714 ) / 42
LCM(546,714) = 389844 / 42
LCM(546,714) = 9282
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 489,800?
The HCF of 489,800 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 489/546, 800/714?
Answer: GCF of Numerators as per given numbers 489/546, 800/714 is
GCF of Numerators i.e. for 489,800 is 1
LCM of denominators i.e. for 546,714 is 9282.
Thus, GCF of Fractions is 1/9282.Finally, GCF of Fractions for 489/546, 800/714 is 1/9282.