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  • Step 1of 5

    Consider

    Recall the definition,

    If a and b are relatively prime, then

    For,

    The set of all positive integers less than 5 are

    Find the integers that are relatively prime to 5.

    But the integer 5 is a prime, therefore each ofis relatively prime to 5.

  • Step 2of 5

    For,

    The set of all positive integers less than 8 are

    Find the integers that are relatively prime to 8.

    The integer 8 can be factored as , so only odd numbers are relatively prime to it.

    The odd numbers that are less than 8 are

    Thus, the positive integers relatively prime to 8 are.

  • Step 3of 5

    For,

    The set of all positive integers less than 8 are

    Find the integers that are relatively prime to 12.

    The integer 12 can be factored as, so any integers that do not have 2 or 3 as factors are relatively prime to 12.

    The integers that are

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    less than 12 and do not have 2 or 3 as factors are

    Thus, the positive integers relatively prime to 12 are.

  • Step 4of 5

    For,

    The set of all positive integers less than 20 are

    Find the integers that are relatively prime to 20.

    The integer 20 can be factored as, so any integers that do not have 2 or 5 as factors are relatively prime to 20.

    The integers that are less than 20 and do not have 2 or 5 as factors are

    Thus, the positive integers relatively prime to 20 are.

  • Step 5of 5

    For,

    The set of all positive integers less than 25 are

    Find the integers that are relatively prime to 25.

    The integer 25 can be factored as, so any integers that do not have 5 as factors are relatively prime to 25.

    The integers that are less than 25 and do not have 5 as factor are

    Thus, the positive integers relatively prime to 20 are

    .


Category: Abstract

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