Use our free GCF of Fractions Calculator tool to compute the GCF of 46/90, 665/90, 420/688 i.e 1/30960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 46/90, 665/90, 420/688.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 46/90,665/90,420/688
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 46/90,665/90,420/688, numerators are 46,665,420
Denominators are 90,90,688
The GCF of 46,665,420 is 1 .
LCM of 90,90,688 is 30960.
The greatest common factor of 46/90,665/90,420/688 = [GCF of 46,665,420]/[LCM of 90,90,688]= 1/30960
Therefore, the GCF of 46/90,665/90,420/688 is 1/30960.
To find the highest common factor of 46,665,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 46 are 1, 2, 23, 46
The factors of 665 are 1, 5, 7, 19, 35, 95, 133, 665
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 46,665,420 is 1.
Lets's calculate GCF of 46,665,420
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 46
:1,2,23,46
Now, list down the factors of 665
:1,5,7,19,35,95,133,665
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 46,665,420 . The biggest common factor number is the GCF number.
So the greatest common factor 46,665,420 is 1.
Lets's calculate LCM of 90,90,688
2 | 90, 90, 688 |
3 | 45, 45, 344 |
3 | 15, 15, 344 |
5 | 5, 5, 344 |
1, 1, 344 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 5 x 1 x 1 x 344 = 30960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30960
Therefore, the GCF of Fractions 46/90,665/90,420/688 is 1/30960
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 90,90,688 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(90,90,688) = 2
common factors(in case of two or more numbers have common factors) = 90
GCF(90,90,688) x common factors =2 x 90 = 180
LCM(90,90,688) = ( 90 × 90 × 688 ) / 180
LCM(90,90,688) = 5572800 / 180
LCM(90,90,688) = 30960
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 46,665,420?
The HCF of 46,665,420 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 46/90, 665/90, 420/688?
Answer: GCF of Numerators as per given numbers 46/90, 665/90, 420/688 is
GCF of Numerators i.e. for 46,665,420 is 1
LCM of denominators i.e. for 90,90,688 is 30960.
Thus, GCF of Fractions is 1/30960.Finally, GCF of Fractions for 46/90, 665/90, 420/688 is 1/30960.