Is 930 a prime number?
It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 930, the answer is: No, 930 is not a prime number.
The list of all positive divisors (i.e., the list of all integers that divide 930) is as follows: 1, 2, 3, 5, 6, 10, 15, 30, 31, 62, 93, 155, 186, 310, 465, 930.
For 930 to be a prime number, it would have been required that 930 has only two divisors, i.e., itself and 1.
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Actually, one can immediately see that 930 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 930 is 0, so it is divisible by 5 and is therefore not prime.
As a consequence:
- 930 is a multiple of 1
- 930 is a multiple of 2
- 930 is a multiple of 3
- 930 is a multiple of 5
- 930 is a multiple of 6
- 930 is a multiple of 10
- 930 is a multiple of 15
- 930 is a multiple of 30
- 930 is a multiple of 31
- 930 is a multiple of 62
- 930 is a multiple of 93
- 930 is a multiple of 155
- 930 is a multiple of 186
- 930 is a multiple of 310
- 930 is a multiple of 465
For 930 to be a prime number, it would have been required that 930 has only two divisors, i.e., itself and 1.
Is 930 a deficient number?
No, 930 is not a deficient number: to be deficient, 930 should have been such that 930 is larger than the sum of its proper divisors, i.e., the divisors of 930 without 930 itself (that is 1 + 2 + 3 + 5 + 6 + 10 + 15 + 30 + 31 + 62 + 93 + 155 + 186 + 310 + 465 = 1 374).
In fact, 930 is an abundant number; 930 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 5 + 6 + 10 + 15 + 30 + 31 + 62 + 93 + 155 + 186 + 310 + 465 = 1 374). The smallest abundant number is 12.