GCF of 407/23, 402/48, 731/96
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 407/23, 402/48, 731/96 i.e 1/2208 easily. The following is the detailed procedure to determine the greatest common factor of fractions 407/23, 402/48, 731/96.
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 407/23,402/48,731/96?
Given fractions are 407/23,402/48,731/96
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 407/23,402/48,731/96, numerators are 407,402,731
Denominators are 23,48,96
The GCF of 407,402,731 is 1 .
LCM of 23,48,96 is 2208.
The greatest common factor of 407/23,402/48,731/96 = [GCF of 407,402,731]/[LCM of 23,48,96]= 1/2208
Therefore, the GCF of 407/23,402/48,731/96 is 1/2208.
To find the highest common factor of 407,402,731, we have to find the factors of both numbers and list the highest common factor.
The factors of 407 are 1, 11, 37, 407
The factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402
The factors of 731 are 1, 17, 43, 731
The HCF of 407,402,731 is 1.
Lets's calculate GCF of 407,402,731
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 407,402,731 By Matching Biggest Common Factor Method
Now, list down the factors of 407
:1,11,37,407
Now, list down the factors of 402
:1,2,3,6,67,134,201,402
Now, list down the factors of 731
:1,17,43,731
Greatest Common Factor
We found the factors 407,402,731 . The biggest common factor number is the GCF number.
So the greatest common factor 407,402,731 is 1.
Lets's calculate LCM of 23,48,96
| 2 | 23, 48, 96 |
| 2 | 23, 24, 48 |
| 2 | 23, 12, 24 |
| 2 | 23, 6, 12 |
| 3 | 23, 3, 6 |
| 23, 1, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 23 x 1 x 2 = 2208
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2208
Therefore, the GCF of Fractions 407/23,402/48,731/96 is 1/2208
Least Common Multiple of 23,48,96 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 23,48,96 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(23,48,96) = 1
common factors(in case of two or more numbers have common factors) = 48
GCF(23,48,96) x common factors =1 x 48 = 48
LCM(23,48,96) = ( 23 × 48 × 96 ) / 48
LCM(23,48,96) = 105984 / 48
LCM(23,48,96) = 2208
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 407/23, 402/48, 731/96
1. What is the HCF of 407,402,731?
The HCF of 407,402,731 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 407/23, 402/48, 731/96?
Answer: GCF of Numerators as per given numbers 407/23, 402/48, 731/96 is
GCF of Numerators i.e. for 407,402,731 is 1
LCM of denominators i.e. for 23,48,96 is 2208.
Thus, GCF of Fractions is 1/2208.Finally, GCF of Fractions for 407/23, 402/48, 731/96 is 1/2208.