Use our free GCF of Fractions Calculator tool to compute the GCF of 45/34, 897/45, 900/714 i.e 3/10710 easily. The following is the detailed procedure to determine the greatest common factor of fractions 45/34, 897/45, 900/714.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 45/34,897/45,900/714
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 45/34,897/45,900/714, numerators are 45,897,900
Denominators are 34,45,714
The GCF of 45,897,900 is 3 .
LCM of 34,45,714 is 10710.
The greatest common factor of 45/34,897/45,900/714 = [GCF of 45,897,900]/[LCM of 34,45,714]= 3/10710
Therefore, the GCF of 45/34,897/45,900/714 is 3/10710.
To find the highest common factor of 45,897,900, we have to find the factors of both numbers and list the highest common factor.
The factors of 45 are 1, 3, 5, 9, 15, 45
The factors of 897 are 1, 3, 13, 23, 39, 69, 299, 897
The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
The HCF of 45,897,900 is 3.
Lets's calculate GCF of 45,897,900
3 | 45, 897, 900 |
15, 299, 300 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 45
:1,3,5,9,15,45
Now, list down the factors of 897
:1,3,13,23,39,69,299,897
Now, list down the factors of 900
:1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450,900
Greatest Common Factor
We found the factors 45,897,900 . The biggest common factor number is the GCF number.
So the greatest common factor 45,897,900 is 3.
Lets's calculate LCM of 34,45,714
2 | 34, 45, 714 |
3 | 17, 45, 357 |
17 | 17, 15, 119 |
1, 15, 7 |
∴ So the LCM of the given numbers is 2 x 3 x 17 x 1 x 15 x 7 = 10710
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/10710
Therefore, the GCF of Fractions 45/34,897/45,900/714 is 3/10710
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 34,45,714 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,45,714) = 1
common factors(in case of two or more numbers have common factors) = 102
GCF(34,45,714) x common factors =1 x 102 = 102
LCM(34,45,714) = ( 34 × 45 × 714 ) / 102
LCM(34,45,714) = 1092420 / 102
LCM(34,45,714) = 10710
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 45,897,900?
The HCF of 45,897,900 is 3
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 45/34, 897/45, 900/714?
Answer: GCF of Numerators as per given numbers 45/34, 897/45, 900/714 is
GCF of Numerators i.e. for 45,897,900 is 3
LCM of denominators i.e. for 34,45,714 is 10710.
Thus, GCF of Fractions is 3/10710.Finally, GCF of Fractions for 45/34, 897/45, 900/714 is 3/10710.