Deficient Number
Definition of Deficient Number

• If the sum of all the proper divisors of a number is less than the number itself, then the number is called a Deficient Number.

More about Deficient Number

• Deficient number is also called as ‘defective number’.
• All prime numbers are defective numbers.

Example of Deficient Number

• Take an example of 14. The proper divisors of 14 are 1, 2, 7.
  Sum of the proper divisors = 1 + 2 + 7 = 10.
  10 is smaller than 14.
  So, 14 is a defective or deficient number.
  

Solved Example on Deficient Number

Identify the defective number from the following.
Choices:
A. 20
B. 12
C. 6
D. 21
Correct Answer: D
Solution:
Step 1: Sum of the proper divisors of 20 = 1 + 2 + 4 + 5 + 10 = 22
Step 2: Sum of the proper divisors of 12 = 1 + 2 + 3 + 4 + 6 = 16
Step 3: Sum of the proper divisors of 6 = 1 + 2 + 3 = 6
Step 4: Sum of the proper divisors of 21 = 1 + 3 + 7 = 11
Step 5: 20, 12, and 6 are not defective numbers as the sum of all the proper divisors of these numbers are not less than the numbers.
Step 6: As sum of all the proper divisors of 21 is less than the number itself, so 21 is a deficient number.

Related Terms for Deficient Number

• Amicable Numbers
• Divisor

Additional Links for Deficient Number

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