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Mathematics Dictionary
Dr. K. G. Shih
Factors of numbers


  • Q01 | - Factors of numbers
  • Q02 | - Amicable number
  • Q03 | - Abundant number
  • Q04 | - Deficient number
  • Q05 | - Perfect number
  • Q06 | - Prime number

    • Q01. Factors of numbers

    Definition
    • 1. Prime number
      • It has only two factors
      • 1 and number itself
    • 2. Abundant number
      • Sum of its factor without number itself
      • The sum is greater number itself
    • 3. Deficient number
      • Sum of its factor without number itself
      • The sum is less number itself
    • 4. Perfect number
      • Sum of its factor without number itself
      • The sum is equal number itself
    • 5. Amicable number
      • Sum of its factor of number n1 without number itself equals n2
      • Sum of its factor of number n2 without number itself equals n1
      • The number pair n1 and n2 are amicable pairs

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    Q02. Amicable number pairs

    Example
    • 1. prove that 220 and 284 are amicable pairs
    • 2. prove that 1184 and 1210 are amicable pairs
    Reference
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    Q03. Abundant number

    Example : Prove that 30 is abundant number
    • Factors without 30
    • Factors of 30 = 1, 2, 3, 5, 6, 10, 15
    • Sum of factors of 30 = 1 + 2 + 3 + 5 + 6 + 10 + 15 = 42
    • Since sum of factors is greater than 30
    • Hence 30 is abundant number
    Reference
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    Q4. Deficient number

    Example : Prove that 27 is deficient number
    • Factors without 27
    • Factors of 27 = 1, 3, 9
    • Sum of factors of 27 = 1 + 3 + 9 = 13
    • Since sum of factors is less than 27
    • Hence 27 is deficient number
    Reference
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    Q5. Perfect number

    Example : Prove that 28 is perfect number
    • Factors without 28
    • Factors of 28 = 1, 2, 4, 7, 14
    • Sum of factors of 30 = 1 + 2 + 4 + 7 + 14 = 28
    • Since sum of factors is equal 28
    • Hence 28 is perfect number
    Reference
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    Q6. Prime number

    Example : Prove that 29 is prime number
    • Factors of 29 : 1 and 29
    • Hence 29 is prime number
    Prime factor of number
    • All factors of a number are prime numbers
    • Example 30 = 2*15 = 2*3*5
    • 2, 3, 5 are prime numbers
    Reference
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