gustavrubioo1010 gustavrubioo1010
  • 03-03-2022
  • Mathematics
contestada

Prove that any number n of the form abcabc, where a, b, and c are decimal digits, is divisible by 7, 11 and 13.

Respuesta :

LammettHash
LammettHash LammettHash
  • 04-03-2022

We can factorize abcabc as

abcabc = abc000 + abc

abcabc = abc (1000 + 1)

abcabc = abc × 1001

abcabc = abc × 7 × 11 × 13

so naturally each of 7, 11, and 13 must divide abcabc.

Answer Link

Otras preguntas

Which period was the “golden age of dinosaurs”? a. the Triassic Period b. the Jurassic Period c. the Cretaceous Period d. the Tyrannosaurus Period
A flight instructor charges $50 per lesson, plus an additional fee for the use of his plane. The charge for the use of the plane varies directly with the square
What are abiotic factors of the enviroment lynx
If ab = 10 and a2 + b2 = 30, what is the value of (a + b)^2?
If it takes Mark twice as long to earn $6.00 as it takes Carl to earn $4.00, what is the ratio of Mark’s pay per hour to Carl’s pay per hour?
A circular pool is ten feet in diameter and five feet deep. What is its volume, in cubic feet?
what does etymology study?
least number that has 2, 3, 4, as factors
Which of the allies suffered the greatest losses on D-Day
which explorer sailed for france?