Is 870 a prime number?
It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 870, the answer is: No, 870 is not a prime number.
The list of all positive divisors (i.e., the list of all integers that divide 870) is as follows: 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870.
For 870 to be a prime number, it would have been required that 870 has only two divisors, i.e., itself and 1.
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Actually, one can immediately see that 870 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 870 is 0, so it is divisible by 5 and is therefore not prime.
As a consequence:
- 870 is a multiple of 1
- 870 is a multiple of 2
- 870 is a multiple of 3
- 870 is a multiple of 5
- 870 is a multiple of 6
- 870 is a multiple of 10
- 870 is a multiple of 15
- 870 is a multiple of 29
- 870 is a multiple of 30
- 870 is a multiple of 58
- 870 is a multiple of 87
- 870 is a multiple of 145
- 870 is a multiple of 174
- 870 is a multiple of 290
- 870 is a multiple of 435
For 870 to be a prime number, it would have been required that 870 has only two divisors, i.e., itself and 1.
Is 870 a deficient number?
No, 870 is not a deficient number: to be deficient, 870 should have been such that 870 is larger than the sum of its proper divisors, i.e., the divisors of 870 without 870 itself (that is 1 + 2 + 3 + 5 + 6 + 10 + 15 + 29 + 30 + 58 + 87 + 145 + 174 + 290 + 435 = 1 290).
In fact, 870 is an abundant number; 870 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 5 + 6 + 10 + 15 + 29 + 30 + 58 + 87 + 145 + 174 + 290 + 435 = 1 290). The smallest abundant number is 12.
