Is 270 a prime number?
It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 270, the answer is: No, 270 is not a prime number.
The list of all positive divisors (i.e., the list of all integers that divide 270) is as follows: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270.
For 270 to be a prime number, it would have been required that 270 has only two divisors, i.e., itself and 1.
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Actually, one can immediately see that 270 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 270 is 0, so it is divisible by 5 and is therefore not prime.
As a consequence:
- 270 is a multiple of 1
- 270 is a multiple of 2
- 270 is a multiple of 3
- 270 is a multiple of 5
- 270 is a multiple of 6
- 270 is a multiple of 9
- 270 is a multiple of 10
- 270 is a multiple of 15
- 270 is a multiple of 18
- 270 is a multiple of 27
- 270 is a multiple of 30
- 270 is a multiple of 45
- 270 is a multiple of 54
- 270 is a multiple of 90
- 270 is a multiple of 135
For 270 to be a prime number, it would have been required that 270 has only two divisors, i.e., itself and 1.
Is 270 a deficient number?
No, 270 is not a deficient number: to be deficient, 270 should have been such that 270 is larger than the sum of its proper divisors, i.e., the divisors of 270 without 270 itself (that is 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 27 + 30 + 45 + 54 + 90 + 135 = 450).
In fact, 270 is an abundant number; 270 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 27 + 30 + 45 + 54 + 90 + 135 = 450). The smallest abundant number is 12.
