gonzo3162 gonzo3162
  • 22-07-2022
  • Mathematics
contestada

Let k be the largest integer such that 343/7^k is an integer. What is the remainder when 343/7^k is divided by 7

Respuesta :

sqdancefan
sqdancefan sqdancefan
  • 02-08-2022

Answer:

  1

Step-by-step explanation:

The given ratio will be the remaining factor of 343 after factors of 7 have been removed. The value of interest is that factor, modulo 7.

Factors of 343

  343 = 7·7·7 = 7³

Ratio

The value of k is the power of 7 in the factorization of 343, so we have ...

  k = 3

and ...

  343/7³ = 1

Remainder

The remainder when this ratio is divided by 7 is ...

  1 mod 7 = 1

The remainder when 343/7^k is divided by 7 is 1.

Answer Link

Otras preguntas

How many days r in a year
why was the Trans-Atlantic slave trade important
who is of the united states president
What invention of the 1900s might have lessened gibraltar's importance as a military base?
What tradition has been largely adopted since 1797
just no time need help on whatever question you wanna answer and explain please im begging
What is the solution of the system? use the substitution method. 3x + 2y = 11 x - 2 = -4y A. The only solution is (12, -5/2) B. The solution is (4, -1/2) C.ther
31 POINTS PLEASE HELP WILL GIVE BRAINLIEST A rental car company charges $15 per day for a rental car plus 20¢ for every mile driven that day. Which equation mod
Despite Thomas Jefferson’s goal of limited government, his administration doubled the size of the United States with the purchase of the Louisiana Territory. Th
Explain metaphor the magistrate sits in your heart that judges you