GCF of 732/742, 408/654
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 732/742, 408/654 i.e 12/242634 easily. The following is the detailed procedure to determine the greatest common factor of fractions 732/742, 408/654.
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 732/742,408/654?
Given fractions are 732/742,408/654
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 732/742,408/654, numerators are 732,408
Denominators are 742,654
The GCF of 732,408 is 12 .
LCM of 742,654 is 242634.
The greatest common factor of 732/742,408/654 = [GCF of 732,408]/[LCM of 742,654]= 12/242634
Therefore, the GCF of 732/742,408/654 is 12/242634.
To find the highest common factor of 732,408, we have to find the factors of both numbers and list the highest common factor.
The factors of 732 are 1, 2, 3, 4, 6, 12, 61, 122, 183, 244, 366, 732
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The HCF of 732,408 is 12.
Lets's calculate GCF of 732,408
| 2 | 732, 408 |
| 2 | 366, 204 |
| 3 | 183, 102 |
| 61, 34 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 732,408 By Matching Biggest Common Factor Method
Now, list down the factors of 732
:1,2,3,4,6,12,61,122,183,244,366,732
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Greatest Common Factor
We found the factors 732,408 . The biggest common factor number is the GCF number.
So the greatest common factor 732,408 is 12.
Lets's calculate LCM of 742,654
| 2 | 742, 654 |
| 371, 327 |
∴ So the LCM of the given numbers is 2 x 371 x 327 = 242634
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/242634
Therefore, the GCF of Fractions 732/742,408/654 is 12/242634
Least Common Multiple of 742,654 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 742,654 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(742,654) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(742,654) x common factors =2 x 1 = 2
LCM(742,654) = ( 742 × 654 ) / 2
LCM(742,654) = 485268 / 2
LCM(742,654) = 242634
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 732/742, 408/654
1. What is the HCF of 732,408?
The HCF of 732,408 is 12
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 732/742, 408/654?
Answer: GCF of Numerators as per given numbers 732/742, 408/654 is
GCF of Numerators i.e. for 732,408 is 12
LCM of denominators i.e. for 742,654 is 242634.
Thus, GCF of Fractions is 12/242634.Finally, GCF of Fractions for 732/742, 408/654 is 12/242634.