It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 157, the answer is: yes, 157 is a prime number because it has only two distinct divisors: 1 and itself (157).
As a consequence, 157 is only a multiple of 1 and 157..
Since 157 is a prime number, 157 is also a deficient number, that is to say 157 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 157 without 157 itself (that is 1, by definition!).
Parity of 157
157 is an odd number, because it is not evenly divisible by 2.
Is 157 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 157 is about 12.530.
Thus, the square root of 157 is not an integer, and therefore 157 is not a square number.
Anyway, 157 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 157?
The square of a number (here 157) is the result of the product of this number (157) by itself (i.e., 157 × 157); the square of 157 is sometimes called "raising 157 to the power 2", or "157 squared".
As a consequence, 157 is the square root of 24 649.
Number of digits of 157
157 is a number with 3 digits.
What are the multiples of 157?
The multiples of 157 are all integers evenly divisible by 157, that is all numbers such that the remainder of the division by 157 is zero. There are infinitely many multiples of 157. The smallest multiples of 157 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 157 too, since 0 × 157 = 0
- 157: indeed, 157 is a multiple of itself, since 157 is evenly divisible by 157 (we have 157 / 157 = 1, so the remainder of this division is indeed zero)
- 314: indeed, 314 = 157 × 2
- 471: indeed, 471 = 157 × 3
- 628: indeed, 628 = 157 × 4
- 785: indeed, 785 = 157 × 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 157). 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 12.530). 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.