GCF of 723/51, 513/149
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 723/51, 513/149 i.e 3/7599 easily. The following is the detailed procedure to determine the greatest common factor of fractions 723/51, 513/149.
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 723/51,513/149?
Given fractions are 723/51,513/149
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 723/51,513/149, numerators are 723,513
Denominators are 51,149
The GCF of 723,513 is 3 .
LCM of 51,149 is 7599.
The greatest common factor of 723/51,513/149 = [GCF of 723,513]/[LCM of 51,149]= 3/7599
Therefore, the GCF of 723/51,513/149 is 3/7599.
To find the highest common factor of 723,513, we have to find the factors of both numbers and list the highest common factor.
The factors of 723 are 1, 3, 241, 723
The factors of 513 are 1, 3, 9, 19, 27, 57, 171, 513
The HCF of 723,513 is 3.
Lets's calculate GCF of 723,513
| 3 | 723, 513 |
| 241, 171 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 723,513 By Matching Biggest Common Factor Method
Now, list down the factors of 723
:1,3,241,723
Now, list down the factors of 513
:1,3,9,19,27,57,171,513
Greatest Common Factor
We found the factors 723,513 . The biggest common factor number is the GCF number.
So the greatest common factor 723,513 is 3.
Lets's calculate LCM of 51,149
Given numbers has no common factors except 1. So, there LCM is their product i.e 7599
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/7599
Therefore, the GCF of Fractions 723/51,513/149 is 3/7599
Least Common Multiple of 51,149 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 51,149 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,149) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(51,149) x common factors =1 x 1 = 1
LCM(51,149) = ( 51 × 149 ) / 1
LCM(51,149) = 7599 / 1
LCM(51,149) = 7599
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FAQs on GCF of Fractions of 723/51, 513/149
1. What is the HCF of 723,513?
The HCF of 723,513 is 3
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 723/51, 513/149?
Answer: GCF of Numerators as per given numbers 723/51, 513/149 is
GCF of Numerators i.e. for 723,513 is 3
LCM of denominators i.e. for 51,149 is 7599.
Thus, GCF of Fractions is 3/7599.Finally, GCF of Fractions for 723/51, 513/149 is 3/7599.