It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 139, the answer is: yes, 139 is a prime number because it has only two distinct divisors: 1 and itself (139).
As a consequence, 139 is only a multiple of 1 and 139..
Since 139 is a prime number, 139 is also a deficient number, that is to say 139 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 139 without 139 itself (that is 1, by definition!).
Parity of 139
139 is an odd number, because it is not evenly divisible by 2.
Is 139 a perfect square number?
A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 139 is about 11.790.
Thus, the square root of 139 is not an integer, and therefore 139 is not a square number.
Anyway, 139 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 139?
The square of a number (here 139) is the result of the product of this number (139) by itself (i.e., 139 × 139); the square of 139 is sometimes called "raising 139 to the power 2", or "139 squared".
As a consequence, 139 is the square root of 19 321.
Number of digits of 139
139 is a number with 3 digits.
What are the multiples of 139?
The multiples of 139 are all integers evenly divisible by 139, that is all numbers such that the remainder of the division by 139 is zero. There are infinitely many multiples of 139. The smallest multiples of 139 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 139 too, since 0 × 139 = 0
- 139: indeed, 139 is a multiple of itself, since 139 is evenly divisible by 139 (we have 139 / 139 = 1, so the remainder of this division is indeed zero)
- 278: indeed, 278 = 139 × 2
- 417: indeed, 417 = 139 × 3
- 556: indeed, 556 = 139 × 4
- 695: indeed, 695 = 139 × 5
How to determine whether an integer is a prime number?
To determine the primality of a number, several algorithms can be used. The most naive technique is to test all divisors strictly smaller to the number of which we want to determine the primality (here 139). First, we can eliminate all even numbers greater than 2 (and hence 4, 6, 8…). Then, we can stop this check when we reach the square root of the number of which we want to determine the primality (here the square root is about 11.790). Historically, the sieve of Eratosthenes (dating from the Greek mathematics) implements this technique in a relatively efficient manner.
More modern techniques include the sieve of Atkin, probabilistic algorithms, and the cyclotomic AKS test.