GCF of 416/82, 897/142
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 416/82, 897/142 i.e 13/5822 easily. The following is the detailed procedure to determine the greatest common factor of fractions 416/82, 897/142.
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 416/82,897/142?
Given fractions are 416/82,897/142
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 416/82,897/142, numerators are 416,897
Denominators are 82,142
The GCF of 416,897 is 13 .
LCM of 82,142 is 5822.
The greatest common factor of 416/82,897/142 = [GCF of 416,897]/[LCM of 82,142]= 13/5822
Therefore, the GCF of 416/82,897/142 is 13/5822.
To find the highest common factor of 416,897, we have to find the factors of both numbers and list the highest common factor.
The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
The factors of 897 are 1, 3, 13, 23, 39, 69, 299, 897
The HCF of 416,897 is 13.
Lets's calculate GCF of 416,897
| 13 | 416, 897 |
| 32, 69 |
∴ So the GCF of the given numbers is 13 = 13
Greatest Common Factor of 416,897 By Matching Biggest Common Factor Method
Now, list down the factors of 416
:1,2,4,8,13,16,26,32,52,104,208,416
Now, list down the factors of 897
:1,3,13,23,39,69,299,897
Greatest Common Factor
We found the factors 416,897 . The biggest common factor number is the GCF number.
So the greatest common factor 416,897 is 13.
Lets's calculate LCM of 82,142
| 2 | 82, 142 |
| 41, 71 |
∴ So the LCM of the given numbers is 2 x 41 x 71 = 5822
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/5822
Therefore, the GCF of Fractions 416/82,897/142 is 13/5822
Least Common Multiple of 82,142 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 82,142 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,142) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(82,142) x common factors =2 x 1 = 2
LCM(82,142) = ( 82 × 142 ) / 2
LCM(82,142) = 11644 / 2
LCM(82,142) = 5822
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 416/82, 897/142
1. What is the HCF of 416,897?
The HCF of 416,897 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 416/82, 897/142?
Answer: GCF of Numerators as per given numbers 416/82, 897/142 is
GCF of Numerators i.e. for 416,897 is 13
LCM of denominators i.e. for 82,142 is 5822.
Thus, GCF of Fractions is 13/5822.Finally, GCF of Fractions for 416/82, 897/142 is 13/5822.