Is 112 a prime number?
It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 112, the answer is: No, 112 is not a prime number.
The list of all positive divisors (i.e., the list of all integers that divide 112) is as follows: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112.
For 112 to be a prime number, it would have been required that 112 has only two divisors, i.e., itself and 1.
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As a consequence:
- 112 is a multiple of 1
- 112 is a multiple of 2
- 112 is a multiple of 4
- 112 is a multiple of 7
- 112 is a multiple of 8
- 112 is a multiple of 14
- 112 is a multiple of 16
- 112 is a multiple of 28
- 112 is a multiple of 56
For 112 to be a prime number, it would have been required that 112 has only two divisors, i.e., itself and 1.
Is 112 a deficient number?
No, 112 is not a deficient number: to be deficient, 112 should have been such that 112 is larger than the sum of its proper divisors, i.e., the divisors of 112 without 112 itself (that is 1 + 2 + 4 + 7 + 8 + 14 + 16 + 28 + 56 = 136).
In fact, 112 is an abundant number; 112 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 7 + 8 + 14 + 16 + 28 + 56 = 136). The smallest abundant number is 12.