Is 690 a prime number?
It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 690, the answer is: No, 690 is not a prime number.
The list of all positive divisors (i.e., the list of all integers that divide 690) is as follows: 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690.
For 690 to be a prime number, it would have been required that 690 has only two divisors, i.e., itself and 1.
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Actually, one can immediately see that 690 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 690 is 0, so it is divisible by 5 and is therefore not prime.
As a consequence:
- 690 is a multiple of 1
- 690 is a multiple of 2
- 690 is a multiple of 3
- 690 is a multiple of 5
- 690 is a multiple of 6
- 690 is a multiple of 10
- 690 is a multiple of 15
- 690 is a multiple of 23
- 690 is a multiple of 30
- 690 is a multiple of 46
- 690 is a multiple of 69
- 690 is a multiple of 115
- 690 is a multiple of 138
- 690 is a multiple of 230
- 690 is a multiple of 345
For 690 to be a prime number, it would have been required that 690 has only two divisors, i.e., itself and 1.
Is 690 a deficient number?
No, 690 is not a deficient number: to be deficient, 690 should have been such that 690 is larger than the sum of its proper divisors, i.e., the divisors of 690 without 690 itself (that is 1 + 2 + 3 + 5 + 6 + 10 + 15 + 23 + 30 + 46 + 69 + 115 + 138 + 230 + 345 = 1 038).
In fact, 690 is an abundant number; 690 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 5 + 6 + 10 + 15 + 23 + 30 + 46 + 69 + 115 + 138 + 230 + 345 = 1 038). The smallest abundant number is 12.
