GCF of 408/39, 759/724
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 408/39, 759/724 i.e 3/28236 easily. The following is the detailed procedure to determine the greatest common factor of fractions 408/39, 759/724.
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 408/39,759/724?
Given fractions are 408/39,759/724
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 408/39,759/724, numerators are 408,759
Denominators are 39,724
The GCF of 408,759 is 3 .
LCM of 39,724 is 28236.
The greatest common factor of 408/39,759/724 = [GCF of 408,759]/[LCM of 39,724]= 3/28236
Therefore, the GCF of 408/39,759/724 is 3/28236.
To find the highest common factor of 408,759, we have to find the factors of both numbers and list the highest common factor.
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The factors of 759 are 1, 3, 11, 23, 33, 69, 253, 759
The HCF of 408,759 is 3.
Lets's calculate GCF of 408,759
| 3 | 408, 759 |
| 136, 253 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 408,759 By Matching Biggest Common Factor Method
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Now, list down the factors of 759
:1,3,11,23,33,69,253,759
Greatest Common Factor
We found the factors 408,759 . The biggest common factor number is the GCF number.
So the greatest common factor 408,759 is 3.
Lets's calculate LCM of 39,724
Given numbers has no common factors except 1. So, there LCM is their product i.e 28236
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/28236
Therefore, the GCF of Fractions 408/39,759/724 is 3/28236
Least Common Multiple of 39,724 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 39,724 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(39,724) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(39,724) x common factors =1 x 1 = 1
LCM(39,724) = ( 39 × 724 ) / 1
LCM(39,724) = 28236 / 1
LCM(39,724) = 28236
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FAQs on GCF of Fractions of 408/39, 759/724
1. What is the HCF of 408,759?
The HCF of 408,759 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 408/39, 759/724?
Answer: GCF of Numerators as per given numbers 408/39, 759/724 is
GCF of Numerators i.e. for 408,759 is 3
LCM of denominators i.e. for 39,724 is 28236.
Thus, GCF of Fractions is 3/28236.Finally, GCF of Fractions for 408/39, 759/724 is 3/28236.