If the sum of the proper divisors of a number is greater than that number, then that number is called as an Abundant Number.
The difference of the sum of the divisors and the number is called �abundance�.
945 is the smallest odd 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.
A. 16
B. 22
C. 9
D. 18
Correct Answer: D
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 <>
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 <>
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.
Q1: Which of the following is an abundant number?
Q2: What is the abundance of the number 12?
Q: What are proper divisors?
A: Proper divisors of a number are all its divisors excluding the number itself.
Q: How do I check if a number is abundant?
A: Find all the proper divisors, sum them, and check if the sum is greater than the original number.