GCF of 744/87, 960/723
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 744/87, 960/723 i.e 24/20967 easily. The following is the detailed procedure to determine the greatest common factor of fractions 744/87, 960/723.
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 744/87,960/723?
Given fractions are 744/87,960/723
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 744/87,960/723, numerators are 744,960
Denominators are 87,723
The GCF of 744,960 is 24 .
LCM of 87,723 is 20967.
The greatest common factor of 744/87,960/723 = [GCF of 744,960]/[LCM of 87,723]= 24/20967
Therefore, the GCF of 744/87,960/723 is 24/20967.
To find the highest common factor of 744,960, we have to find the factors of both numbers and list the highest common factor.
The factors of 744 are 1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 124, 186, 248, 372, 744
The factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
The HCF of 744,960 is 24.
Lets's calculate GCF of 744,960
| 2 | 744, 960 |
| 2 | 372, 480 |
| 2 | 186, 240 |
| 3 | 93, 120 |
| 31, 40 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
Greatest Common Factor of 744,960 By Matching Biggest Common Factor Method
Now, list down the factors of 744
:1,2,3,4,6,8,12,24,31,62,93,124,186,248,372,744
Now, list down the factors of 960
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,64,80,96,120,160,192,240,320,480,960
Greatest Common Factor
We found the factors 744,960 . The biggest common factor number is the GCF number.
So the greatest common factor 744,960 is 24.
Lets's calculate LCM of 87,723
| 3 | 87, 723 |
| 29, 241 |
∴ So the LCM of the given numbers is 3 x 29 x 241 = 20967
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/20967
Therefore, the GCF of Fractions 744/87,960/723 is 24/20967
Least Common Multiple of 87,723 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 87,723 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(87,723) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(87,723) x common factors =3 x 1 = 3
LCM(87,723) = ( 87 × 723 ) / 3
LCM(87,723) = 62901 / 3
LCM(87,723) = 20967
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FAQs on GCF of Fractions of 744/87, 960/723
1. What is the HCF of 744,960?
The HCF of 744,960 is 24
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 744/87, 960/723?
Answer: GCF of Numerators as per given numbers 744/87, 960/723 is
GCF of Numerators i.e. for 744,960 is 24
LCM of denominators i.e. for 87,723 is 20967.
Thus, GCF of Fractions is 24/20967.Finally, GCF of Fractions for 744/87, 960/723 is 24/20967.