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Abundant Number
Definition of Abundant Number
 If the sum of the proper divisors of a number is greater than that number, then that number is called as an Abundant Number.
More about Abundant Number
 The difference of the sum of the divisors and the number is called abundance.
 945 is the smallest odd abundant number.
Examples of Abundant Number
 Consider the number 12. The proper divisors of 12 are 1, 2, 3, 4, and 6. Sum of these divisors = 1 + 2 + 3 + 4 + 6 = 16. As the sum of the divisors is 16 and 16 is greater than 12, so 12 is an abundant number.
 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100 are the list of abundant numbers between 1 and 100.
Solved Example on Abundant Number
Which of the following satisfies the abundant number property?
Choices:
A. 16
B. 22
C. 9
D. 18
Correct Answer: D
Solution:
Step 1: If the sum of the proper divisors of a number is greater than that number, then that number is called as an abundant number.
Step 2: The proper divisors of 16 are 1, 2, 4, and 8.
1 + 2 + 4 + 8 = 15, the sum of the divisors of the number 16 is not greater than the number.????????? [15 < 16.]
Step 3: The proper divisors of 22 are 1, 2, and 11.
1 + 2 + 11 = 14, the sum of the divisors of the number 22 is not greater than the number. [14 < 22.]
Step 4: The proper divisors of 9 are 1 and 3.
1 + 3 = 4, the sum of the divisors of the number 9 is not greater than the number.? [4 < 9.]
Step 5: The proper divisors of 18 are 1, 2, 3, 6, and 9.
1 + 2 + 3 + 6 + 9 = 21, the sum of the divisors of the number 16 is greater than the number.????????? [21 > 18.]
Step 6: So, the number 18 satisfies the abundant number property.
Related Terms for Abundant Number
 Addition
 Divisor
 Even Number
 Factors
 Greater than
 Odd Number
 Proper Divisor
Additional Links for Abundant Number
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