Is 450 a prime number?
It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 450, the answer is: No, 450 is not a prime number.
The list of all positive divisors (i.e., the list of all integers that divide 450) is as follows: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450.
For 450 to be a prime number, it would have been required that 450 has only two divisors, i.e., itself and 1.
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Actually, one can immediately see that 450 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 450 is 0, so it is divisible by 5 and is therefore not prime.
As a consequence:
- 450 is a multiple of 1
- 450 is a multiple of 2
- 450 is a multiple of 3
- 450 is a multiple of 5
- 450 is a multiple of 6
- 450 is a multiple of 9
- 450 is a multiple of 10
- 450 is a multiple of 15
- 450 is a multiple of 18
- 450 is a multiple of 25
- 450 is a multiple of 30
- 450 is a multiple of 45
- 450 is a multiple of 50
- 450 is a multiple of 75
- 450 is a multiple of 90
- 450 is a multiple of 150
- 450 is a multiple of 225
For 450 to be a prime number, it would have been required that 450 has only two divisors, i.e., itself and 1.
Is 450 a deficient number?
No, 450 is not a deficient number: to be deficient, 450 should have been such that 450 is larger than the sum of its proper divisors, i.e., the divisors of 450 without 450 itself (that is 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 25 + 30 + 45 + 50 + 75 + 90 + 150 + 225 = 759).
In fact, 450 is an abundant number; 450 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 25 + 30 + 45 + 50 + 75 + 90 + 150 + 225 = 759). The smallest abundant number is 12.
