Education Technology

A Prime Investigation with 7, 11, and 13

Published on 06/09/2008

Activity Overview

Students investigate the divisibility of 7, 11, and 13. They will also discover an interesting characteristic of six-digit multiples of 1001.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 25 - 29 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Choose any three-digit number, repeat the three digits in the same order to form a six-digit number
  • Enter the number on the calculator and check if it is divisible by 7, 11, and 13
  • Repeat the activity with other three-digit numbers
  • Divide the six-digit number by the product of 7, 11, and 13
  • Observe that the result of the division is the original three-digit number
  • Multiply the product of 7, 11, and 13 with the three-digit number
  • Observe that the result of the multiplication is the original six-digit number
  • Write divisibility tests for 2, 3, and 5


  • Divisibility by 7
  • Take all but the last digit and form a number
  • Subtract twice the units digit from the number formed
  • Continue this process until the remainder is divisible by 7


  • Divisibility by 11
  • Take the sum of every other digit
  • Take the positive difference in the two sums and see if the answer is divisible by 11
  • After the Activity

    Students will complete the Student Worksheet and analyze the results.

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary