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How do you determine if a number is abundant or deficient?
This leads to the Greek classification of numbers as follows:
- If P(n) > n, then n is called an abundant number.
- If P(n) < n, then n is called a deficient number.
- If P(n) = n, then n is called a perfect number.
Is 63 an abundant number?
The first 28 abundant numbers are: 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120. Because 36 is greater than 24, the number 24 is abundant. Its abundance is 36 − 24 = 12.
What is deficient number in math?
In number theory, a deficient number or defective number is a number n for which the sum of divisors of n is less than 2n. For example, the proper divisors of 8 are 1, 2, and 4, and their sum is less than 8, so 8 is deficient.
Is 10 abundant deficient or perfect?
Deficient numbers occur more frequently than abundant numbers. In other words, the sum of the proper divisors of most numbers is less than the numbers themselves. Examples of deficient numbers include 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, and 23.
Is 32 abundant or deficient?
For example, 24 is abundant, its divisors giving a sum of 36; 32 is deficient, giving a sum…
Is 22 abundant deficient or perfect?
Are there more abundant or deficient numbers?
Is 22 a deficient number?
. For example, 22 is deficient because its proper factors sum to 14 < 22. The smallest deficient numbers are 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, and 17.
Is 12 an abundant or deficient number?
Because the sum of its proper divisors (1 + 2 + 3 + 4 + 6 = 16) is greater than 12, 12 is an abundant number. Numbers like 8, whose proper divisors have a sum that is less than the number itself, are called deficient or defective.
How do you know if a number is abundant or excessive?
If the sum of the proper divisors of a number is greater than the number itself, then the number is called abundant or excessive. The proper divisors of 12 are 1, 2, 3, 4, and 6. Because the sum of its proper divisors (1 + 2 + 3 + 4 + 6 = 16) is greater than 12, 12 is an abundant number.
What is the first 5 most abundant numbers?
Twelve is the first abundant number. The next abundant number is 18 because the proper divisors sum to 21 (1 + 2 + 3 + 6 + 9). The first five abundant numbers are 12, 18, 20, 24, and 30.
What is an example of deficient number?
In other words, the sum of the proper divisors of most numbers is less than the numbers themselves. Examples of deficient numbers include 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, and 23.