GCF of 742/51, 304/729
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 742/51, 304/729 i.e 2/12393 easily. The following is the detailed procedure to determine the greatest common factor of fractions 742/51, 304/729.
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 742/51,304/729?
Given fractions are 742/51,304/729
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 742/51,304/729, numerators are 742,304
Denominators are 51,729
The GCF of 742,304 is 2 .
LCM of 51,729 is 12393.
The greatest common factor of 742/51,304/729 = [GCF of 742,304]/[LCM of 51,729]= 2/12393
Therefore, the GCF of 742/51,304/729 is 2/12393.
To find the highest common factor of 742,304, we have to find the factors of both numbers and list the highest common factor.
The factors of 742 are 1, 2, 7, 14, 53, 106, 371, 742
The factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304
The HCF of 742,304 is 2.
Lets's calculate GCF of 742,304
| 2 | 742, 304 |
| 371, 152 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 742,304 By Matching Biggest Common Factor Method
Now, list down the factors of 742
:1,2,7,14,53,106,371,742
Now, list down the factors of 304
:1,2,4,8,16,19,38,76,152,304
Greatest Common Factor
We found the factors 742,304 . The biggest common factor number is the GCF number.
So the greatest common factor 742,304 is 2.
Lets's calculate LCM of 51,729
| 3 | 51, 729 |
| 17, 243 |
∴ So the LCM of the given numbers is 3 x 17 x 243 = 12393
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/12393
Therefore, the GCF of Fractions 742/51,304/729 is 2/12393
Least Common Multiple of 51,729 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 51,729 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,729) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(51,729) x common factors =3 x 1 = 3
LCM(51,729) = ( 51 × 729 ) / 3
LCM(51,729) = 37179 / 3
LCM(51,729) = 12393
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FAQs on GCF of Fractions of 742/51, 304/729
1. What is the HCF of 742,304?
The HCF of 742,304 is 2
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 742/51, 304/729?
Answer: GCF of Numerators as per given numbers 742/51, 304/729 is
GCF of Numerators i.e. for 742,304 is 2
LCM of denominators i.e. for 51,729 is 12393.
Thus, GCF of Fractions is 2/12393.Finally, GCF of Fractions for 742/51, 304/729 is 2/12393.