GCF of 897/414, 9659/722
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 897/414, 9659/722 i.e 13/149454 easily. The following is the detailed procedure to determine the greatest common factor of fractions 897/414, 9659/722.
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 897/414,9659/722?
Given fractions are 897/414,9659/722
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 897/414,9659/722, numerators are 897,9659
Denominators are 414,722
The GCF of 897,9659 is 13 .
LCM of 414,722 is 149454.
The greatest common factor of 897/414,9659/722 = [GCF of 897,9659]/[LCM of 414,722]= 13/149454
Therefore, the GCF of 897/414,9659/722 is 13/149454.
To find the highest common factor of 897,9659, we have to find the factors of both numbers and list the highest common factor.
The factors of 897 are 1, 3, 13, 23, 39, 69, 299, 897
The factors of 9659 are 1, 13, 743, 9659
The HCF of 897,9659 is 13.
Lets's calculate GCF of 897,9659
| 13 | 897, 9659 |
| 69, 743 |
∴ So the GCF of the given numbers is 13 = 13
Greatest Common Factor of 897,9659 By Matching Biggest Common Factor Method
Now, list down the factors of 897
:1,3,13,23,39,69,299,897
Now, list down the factors of 9659
:1,13,743,9659
Greatest Common Factor
We found the factors 897,9659 . The biggest common factor number is the GCF number.
So the greatest common factor 897,9659 is 13.
Lets's calculate LCM of 414,722
| 2 | 414, 722 |
| 207, 361 |
∴ So the LCM of the given numbers is 2 x 207 x 361 = 149454
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/149454
Therefore, the GCF of Fractions 897/414,9659/722 is 13/149454
Least Common Multiple of 414,722 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 414,722 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,722) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(414,722) x common factors =2 x 1 = 2
LCM(414,722) = ( 414 × 722 ) / 2
LCM(414,722) = 298908 / 2
LCM(414,722) = 149454
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FAQs on GCF of Fractions of 897/414, 9659/722
1. What is the HCF of 897,9659?
The HCF of 897,9659 is 13
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 897/414, 9659/722?
Answer: GCF of Numerators as per given numbers 897/414, 9659/722 is
GCF of Numerators i.e. for 897,9659 is 13
LCM of denominators i.e. for 414,722 is 149454.
Thus, GCF of Fractions is 13/149454.Finally, GCF of Fractions for 897/414, 9659/722 is 13/149454.