Is 153 a prime number? What are the divisors of 153?

## Parity of 153

153 is an odd number, because it is not evenly divisible by 2.

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## Is 153 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 153 is about 12.369.

Thus, the square root of 153 is not an integer, and therefore 153 is not a square number.

## What is the square number of 153?

The square of a number (here 153) is the result of the product of this number (153) by itself (i.e., 153 × 153); the square of 153 is sometimes called "raising 153 to the power 2", or "153 squared".

The square of 153 is 23 409 because 153 × 153 = 1532 = 23 409.

As a consequence, 153 is the square root of 23 409.

## Number of digits of 153

153 is a number with 3 digits.

## What are the multiples of 153?

The multiples of 153 are all integers evenly divisible by 153, that is all numbers such that the remainder of the division by 153 is zero. There are infinitely many multiples of 153. The smallest multiples of 153 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 153 too, since 0 × 153 = 0
• 153: indeed, 153 is a multiple of itself, since 153 is evenly divisible by 153 (we have 153 / 153 = 1, so the remainder of this division is indeed zero)
• 306: indeed, 306 = 153 × 2
• 459: indeed, 459 = 153 × 3
• 612: indeed, 612 = 153 × 4
• 765: indeed, 765 = 153 × 5
• etc.

## 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 153). 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 12.369). 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.

## Numbers near 153

• Preceding numbers: …151, 152
• Following numbers: 154, 155

### Nearest numbers from 153

• Preceding prime number: 151
• Following prime number: 157
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