A six-place number is formed by repeating a three-place number; for example, 256,256, or 678,678, etc. Any number of this form is always exactly divisible by:

1951 AMC 12 Problem 19

Attempt Problem 19 of the 1951 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1951 AMC 12 solutions, or check the answer key.

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19.

A six-place number is formed by repeating a three-place number; for example,

256{,}256,

678{,}678,

etc. Any number of this form is always exactly divisible by:

7

only

11

only

13

only

101

1001

Represent the repeated three-digit block by

N

The six-digit number is

1000N+N

If the repeated block is

N,

then the six-place number is

1000N+N=1001N.

It is therefore always divisible by

1001.

Thus, the correct answer is E.