GCF of 725/969, 406/984
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 725/969, 406/984 i.e 29/317832 easily. The following is the detailed procedure to determine the greatest common factor of fractions 725/969, 406/984.
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 725/969,406/984?
Given fractions are 725/969,406/984
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 725/969,406/984, numerators are 725,406
Denominators are 969,984
The GCF of 725,406 is 29 .
LCM of 969,984 is 317832.
The greatest common factor of 725/969,406/984 = [GCF of 725,406]/[LCM of 969,984]= 29/317832
Therefore, the GCF of 725/969,406/984 is 29/317832.
To find the highest common factor of 725,406, we have to find the factors of both numbers and list the highest common factor.
The factors of 725 are 1, 5, 25, 29, 145, 725
The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406
The HCF of 725,406 is 29.
Lets's calculate GCF of 725,406
| 29 | 725, 406 |
| 25, 14 |
∴ So the GCF of the given numbers is 29 = 29
Greatest Common Factor of 725,406 By Matching Biggest Common Factor Method
Now, list down the factors of 725
:1,5,25,29,145,725
Now, list down the factors of 406
:1,2,7,14,29,58,203,406
Greatest Common Factor
We found the factors 725,406 . The biggest common factor number is the GCF number.
So the greatest common factor 725,406 is 29.
Lets's calculate LCM of 969,984
| 3 | 969, 984 |
| 323, 328 |
∴ So the LCM of the given numbers is 3 x 323 x 328 = 317832
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 29/317832
Therefore, the GCF of Fractions 725/969,406/984 is 29/317832
Least Common Multiple of 969,984 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 969,984 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(969,984) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(969,984) x common factors =3 x 1 = 3
LCM(969,984) = ( 969 × 984 ) / 3
LCM(969,984) = 953496 / 3
LCM(969,984) = 317832
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FAQs on GCF of Fractions of 725/969, 406/984
1. What is the HCF of 725,406?
The HCF of 725,406 is 29
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 725/969, 406/984?
Answer: GCF of Numerators as per given numbers 725/969, 406/984 is
GCF of Numerators i.e. for 725,406 is 29
LCM of denominators i.e. for 969,984 is 317832.
Thus, GCF of Fractions is 29/317832.Finally, GCF of Fractions for 725/969, 406/984 is 29/317832.