Is 630 a prime number?
It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 630, the answer is: No, 630 is not a prime number.
The list of all positive divisors (i.e., the list of all integers that divide 630) is as follows: 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630.
For 630 to be a prime number, it would have been required that 630 has only two divisors, i.e., itself and 1.
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Actually, one can immediately see that 630 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 630 is 0, so it is divisible by 5 and is therefore not prime.
As a consequence:
- 630 is a multiple of 1
- 630 is a multiple of 2
- 630 is a multiple of 3
- 630 is a multiple of 5
- 630 is a multiple of 6
- 630 is a multiple of 7
- 630 is a multiple of 9
- 630 is a multiple of 10
- 630 is a multiple of 14
- 630 is a multiple of 15
- 630 is a multiple of 18
- 630 is a multiple of 21
- 630 is a multiple of 30
- 630 is a multiple of 35
- 630 is a multiple of 42
- 630 is a multiple of 45
- 630 is a multiple of 63
- 630 is a multiple of 70
- 630 is a multiple of 90
- 630 is a multiple of 105
- 630 is a multiple of 126
- 630 is a multiple of 210
- 630 is a multiple of 315
For 630 to be a prime number, it would have been required that 630 has only two divisors, i.e., itself and 1.
Is 630 a deficient number?
No, 630 is not a deficient number: to be deficient, 630 should have been such that 630 is larger than the sum of its proper divisors, i.e., the divisors of 630 without 630 itself (that is 1 + 2 + 3 + 5 + 6 + 7 + 9 + 10 + 14 + 15 + 18 + 21 + 30 + 35 + 42 + 45 + 63 + 70 + 90 + 105 + 126 + 210 + 315 = 1 242).
In fact, 630 is an abundant number; 630 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 5 + 6 + 7 + 9 + 10 + 14 + 15 + 18 + 21 + 30 + 35 + 42 + 45 + 63 + 70 + 90 + 105 + 126 + 210 + 315 = 1 242). The smallest abundant number is 12.