GCF of 165/34, 840/854
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 165/34, 840/854 i.e 15/14518 easily. The following is the detailed procedure to determine the greatest common factor of fractions 165/34, 840/854.
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 165/34,840/854?
Given fractions are 165/34,840/854
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 165/34,840/854, numerators are 165,840
Denominators are 34,854
The GCF of 165,840 is 15 .
LCM of 34,854 is 14518.
The greatest common factor of 165/34,840/854 = [GCF of 165,840]/[LCM of 34,854]= 15/14518
Therefore, the GCF of 165/34,840/854 is 15/14518.
To find the highest common factor of 165,840, we have to find the factors of both numbers and list the highest common factor.
The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
The HCF of 165,840 is 15.
Lets's calculate GCF of 165,840
| 3 | 165, 840 |
| 5 | 55, 280 |
| 11, 56 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 165,840 By Matching Biggest Common Factor Method
Now, list down the factors of 165
:1,3,5,11,15,33,55,165
Now, list down the factors of 840
:1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Greatest Common Factor
We found the factors 165,840 . The biggest common factor number is the GCF number.
So the greatest common factor 165,840 is 15.
Lets's calculate LCM of 34,854
| 2 | 34, 854 |
| 17, 427 |
∴ So the LCM of the given numbers is 2 x 17 x 427 = 14518
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/14518
Therefore, the GCF of Fractions 165/34,840/854 is 15/14518
Least Common Multiple of 34,854 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 34,854 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,854) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(34,854) x common factors =2 x 1 = 2
LCM(34,854) = ( 34 × 854 ) / 2
LCM(34,854) = 29036 / 2
LCM(34,854) = 14518
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 165/34, 840/854
1. What is the HCF of 165,840?
The HCF of 165,840 is 15
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 165/34, 840/854?
Answer: GCF of Numerators as per given numbers 165/34, 840/854 is
GCF of Numerators i.e. for 165,840 is 15
LCM of denominators i.e. for 34,854 is 14518.
Thus, GCF of Fractions is 15/14518.Finally, GCF of Fractions for 165/34, 840/854 is 15/14518.