GCF of 829/13, 368/20, 858/16
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 829/13, 368/20, 858/16 i.e 1/1040 easily. The following is the detailed procedure to determine the greatest common factor of fractions 829/13, 368/20, 858/16.
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 829/13,368/20,858/16?
Given fractions are 829/13,368/20,858/16
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 829/13,368/20,858/16, numerators are 829,368,858
Denominators are 13,20,16
The GCF of 829,368,858 is 1 .
LCM of 13,20,16 is 1040.
The greatest common factor of 829/13,368/20,858/16 = [GCF of 829,368,858]/[LCM of 13,20,16]= 1/1040
Therefore, the GCF of 829/13,368/20,858/16 is 1/1040.
To find the highest common factor of 829,368,858, we have to find the factors of both numbers and list the highest common factor.
The factors of 829 are 1, 829
The factors of 368 are 1, 2, 4, 8, 16, 23, 46, 92, 184, 368
The factors of 858 are 1, 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 143, 286, 429, 858
The HCF of 829,368,858 is 1.
Lets's calculate GCF of 829,368,858
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 829,368,858 By Matching Biggest Common Factor Method
Now, list down the factors of 829
:1,829
Now, list down the factors of 368
:1,2,4,8,16,23,46,92,184,368
Now, list down the factors of 858
:1,2,3,6,11,13,22,26,33,39,66,78,143,286,429,858
Greatest Common Factor
We found the factors 829,368,858 . The biggest common factor number is the GCF number.
So the greatest common factor 829,368,858 is 1.
Lets's calculate LCM of 13,20,16
| 2 | 13, 20, 16 |
| 2 | 13, 10, 8 |
| 13, 5, 4 |
∴ So the LCM of the given numbers is 2 x 2 x 13 x 5 x 4 = 1040
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1040
Therefore, the GCF of Fractions 829/13,368/20,858/16 is 1/1040
Least Common Multiple of 13,20,16 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 13,20,16 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(13,20,16) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(13,20,16) x common factors =1 x 4 = 4
LCM(13,20,16) = ( 13 × 20 × 16 ) / 4
LCM(13,20,16) = 4160 / 4
LCM(13,20,16) = 1040
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 829/13, 368/20, 858/16
1. What is the HCF of 829,368,858?
The HCF of 829,368,858 is 1
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 829/13, 368/20, 858/16?
Answer: GCF of Numerators as per given numbers 829/13, 368/20, 858/16 is
GCF of Numerators i.e. for 829,368,858 is 1
LCM of denominators i.e. for 13,20,16 is 1040.
Thus, GCF of Fractions is 1/1040.Finally, GCF of Fractions for 829/13, 368/20, 858/16 is 1/1040.