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72 is an abundant number because the sum of its positive divisors, not including 72 itself, is larger than 72.
Positive divisors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 36 = 123 > 72
(if an integer is larger than the sum of its positive divisors , not including the integer itself, then that integer is called a deficient number, such as prime or power of prime numbers or numbers like 10 are).
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Is 55 a deficient number or a abundant number?
abundant
Can an Abundant number be a prime number?
No, all prime numbers are deficient.
Is 24 a perfect number or abundant number or a deficient number?
A perfect number is a number with factors (excluding itself) that add up to the original number. An abundant number is where this sum is greater than the original number. A deficient number is where the sum is less than the original number. In the case of 24, the factors are 1, 2, 3, 4, 6, 8, 12 and 24. Summing the factors (apart from 24) gives us 1+2+3+4+6+8+12 which equals 36. This is greater than 24, the original number, and so 24 is an abundant number.
Is any prime number have to be deficient?
All prime numbers are deficient.
Are all multiples of abundant numbers abundant?
Yes, this is well known. All integral multiples of any perfect, or abundant number must be an abundant number.
