GCF of 901/105, 814/840, 456/408
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 901/105, 814/840, 456/408 i.e 1/14280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 901/105, 814/840, 456/408.
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 901/105,814/840,456/408?
Given fractions are 901/105,814/840,456/408
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 901/105,814/840,456/408, numerators are 901,814,456
Denominators are 105,840,408
The GCF of 901,814,456 is 1 .
LCM of 105,840,408 is 14280.
The greatest common factor of 901/105,814/840,456/408 = [GCF of 901,814,456]/[LCM of 105,840,408]= 1/14280
Therefore, the GCF of 901/105,814/840,456/408 is 1/14280.
To find the highest common factor of 901,814,456, we have to find the factors of both numbers and list the highest common factor.
The factors of 901 are 1, 17, 53, 901
The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814
The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
The HCF of 901,814,456 is 1.
Lets's calculate GCF of 901,814,456
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 901,814,456 By Matching Biggest Common Factor Method
Now, list down the factors of 901
:1,17,53,901
Now, list down the factors of 814
:1,2,11,22,37,74,407,814
Now, list down the factors of 456
:1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456
Greatest Common Factor
We found the factors 901,814,456 . The biggest common factor number is the GCF number.
So the greatest common factor 901,814,456 is 1.
Lets's calculate LCM of 105,840,408
| 2 | 105, 840, 408 |
| 2 | 105, 420, 204 |
| 2 | 105, 210, 102 |
| 3 | 105, 105, 51 |
| 5 | 35, 35, 17 |
| 7 | 7, 7, 17 |
| 1, 1, 17 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 7 x 1 x 1 x 17 = 14280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/14280
Therefore, the GCF of Fractions 901/105,814/840,456/408 is 1/14280
Least Common Multiple of 105,840,408 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 105,840,408 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(105,840,408) = 3
common factors(in case of two or more numbers have common factors) = 840
GCF(105,840,408) x common factors =3 x 840 = 2520
LCM(105,840,408) = ( 105 × 840 × 408 ) / 2520
LCM(105,840,408) = 35985600 / 2520
LCM(105,840,408) = 14280
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 901/105, 814/840, 456/408
1. What is the HCF of 901,814,456?
The HCF of 901,814,456 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 901/105, 814/840, 456/408?
Answer: GCF of Numerators as per given numbers 901/105, 814/840, 456/408 is
GCF of Numerators i.e. for 901,814,456 is 1
LCM of denominators i.e. for 105,840,408 is 14280.
Thus, GCF of Fractions is 1/14280.Finally, GCF of Fractions for 901/105, 814/840, 456/408 is 1/14280.