157 is an odd number, because it is not evenly divisible by 2.
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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".
The square of 157 is 24 649 because 157 × 157 = 1572 = 24 649.
As a consequence, 157 is the square root of 24 649.
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.
Nearest numbers from 157
- Preceding prime number: 151
- Following prime number: 163