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Grade 11 Challenge: Number Theory & Secret Codes Worksheet with Answers

Grade 11 (US) · Year 12 (UK) · Class 11 (India) · Math

Unit 8: Going FurtherReal-World ChallengesChallenge

Modular arithmetic at work: card and ISBN check digits, toy RSA keys, last digits of huge powers and calendar puzzles. This free high school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

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Challenge: Number Theory & Secret Codes

Grade 11 · Math

Score___ / 12

Name

Class

Date

Learning goal: Real-World Challenges

Directions: Solve each problem. Show your work, then write your answer in the box.

Example

How many zeros are at the end of 758! (758 factorial)?

Answer: 188

  1. 1

    A farmer counts her eggs in 3s and has 2 left over, in 5s and has 4 left over, and in 7s and has 6 left over. What is the smallest positive number of eggs she could have?

    Show your work
    Answer
  2. 2

    How many positive whole numbers divide exactly into 180?

    Answer
  3. 3

    Card numbers end with a Luhn check digit. What check digit completes the (made-up) card number 4650 4770 3600 600_ ?

    Show your work
    Answer
  4. 4

    How many positive whole numbers divide exactly into 5184?

    Answer
  5. 5

    A farmer counts her eggs in 3s and has 2 left over, in 5s and has 2 left over, and in 7s and has 3 left over. What is the smallest positive number of eggs she could have?

    Show your work
    Answer
  6. 6

    What are the last two digits of 7^1358?

    Answer
  7. 7

    How many positive whole numbers divide exactly into 162000?

    Answer
  8. 8

    Toy RSA: p = 7, q = 11, so n = 77 and φ(n) = 60. The public exponent is e = 11. Find the private key d (0 < d < 60) with e·d ≡ 1 (mod 60).

    Show your work
    Answer
  9. 9

    How many zeros are at the end of 332! (332 factorial)?

    Answer
  10. 10

    How many zeros are at the end of 1331! (1331 factorial)?

    Answer
  11. 11

    What are the last two digits of 7^1546?

    Answer
  12. 12

    ISBN-13 check digit: multiply the first 12 digits alternately by 1 and 3, add them up, and the check digit makes the total a multiple of 10. What is the check digit of 978-086835751-_ ?

    Show your work
    Answer

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Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/11/challenge_number_codes

Answer key (click to show)
  1. 1.104
  2. 2.18
  3. 3.0
  4. 4.35
  5. 5.17
  6. 6.49
  7. 7.100
  8. 8.11
  9. 9.81
  10. 10.331
  11. 11.49
  12. 12.5

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