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

why did farmers follow railroads into the texas frontier
THE FULL MOON TURNED ORANGE AND THEN GOT REALLY DARK WHAT COULD HAVE MADE IT TURN DARK LIKE THAT
What did Enlightenment thinkers believe predated society and was superior to the laws of the church or the state?
what is the additive inverse opposite of 18/23
In a parallelogram, one angle is 9 times the size of another. Find the measures of the angles.
how do I solve for x in x^2 - 8x + 12 = 0 using factoring?
What is x^2+8x-5 in vertex form? Please explain.
Which pronoun correctly completes the elliptical clause? You folded fewer towels than __________. A. him B. he
what is the formula for a cylinder and a circle?
the bases of a softball field are 60 feet apart. How far apart is home plate from second base?