GCF of 442/51, 728/744
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 442/51, 728/744 i.e 26/12648 easily. The following is the detailed procedure to determine the greatest common factor of fractions 442/51, 728/744.
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 442/51,728/744?
Given fractions are 442/51,728/744
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 442/51,728/744, numerators are 442,728
Denominators are 51,744
The GCF of 442,728 is 26 .
LCM of 51,744 is 12648.
The greatest common factor of 442/51,728/744 = [GCF of 442,728]/[LCM of 51,744]= 26/12648
Therefore, the GCF of 442/51,728/744 is 26/12648.
To find the highest common factor of 442,728, we have to find the factors of both numbers and list the highest common factor.
The factors of 442 are 1, 2, 13, 17, 26, 34, 221, 442
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The HCF of 442,728 is 26.
Lets's calculate GCF of 442,728
| 2 | 442, 728 |
| 13 | 221, 364 |
| 17, 28 |
∴ So the GCF of the given numbers is 2 x 13 = 26
Greatest Common Factor of 442,728 By Matching Biggest Common Factor Method
Now, list down the factors of 442
:1,2,13,17,26,34,221,442
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Greatest Common Factor
We found the factors 442,728 . The biggest common factor number is the GCF number.
So the greatest common factor 442,728 is 26.
Lets's calculate LCM of 51,744
| 3 | 51, 744 |
| 17, 248 |
∴ So the LCM of the given numbers is 3 x 17 x 248 = 12648
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 26/12648
Therefore, the GCF of Fractions 442/51,728/744 is 26/12648
Least Common Multiple of 51,744 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 51,744 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,744) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(51,744) x common factors =3 x 1 = 3
LCM(51,744) = ( 51 × 744 ) / 3
LCM(51,744) = 37944 / 3
LCM(51,744) = 12648
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FAQs on GCF of Fractions of 442/51, 728/744
1. What is the HCF of 442,728?
The HCF of 442,728 is 26
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 442/51, 728/744?
Answer: GCF of Numerators as per given numbers 442/51, 728/744 is
GCF of Numerators i.e. for 442,728 is 26
LCM of denominators i.e. for 51,744 is 12648.
Thus, GCF of Fractions is 26/12648.Finally, GCF of Fractions for 442/51, 728/744 is 26/12648.