Is 172 a prime number? What are the divisors of 172?

## Is 172 a prime number?

It is possible to find out using mathematical methods whether a given integer is a prime number or not.

For 172, the answer is: No, 172 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 172) is as follows: 1, 2, 4, 43, 86, 172.

To be 172 a prime number, it would have been required that 172 has only two divisors, i.e., itself and 1.

As a consequence:

• 172 is a multiple of 1
• 172 is a multiple of 2
• 172 is a multiple of 4
• 172 is a multiple of 43
• 172 is a multiple of 86

To be 172 a prime number, it would have been required that 172 has only two divisors, i.e., itself and 1.

## Is 172 a deficient number?

Yes, 172 is a deficient number, that is to say 172 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 172 without 172 itself (that is 1 + 2 + 4 + 43 + 86 = 136).

## Parity of 172

172 is an even number, because it is evenly divisible by 2: 172 / 2 = 86.

## Is 172 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 172 is about 13.115.

Thus, the square root of 172 is not an integer, and therefore 172 is not a square number.

## What is the square number of 172?

The square of a number (here 172) is the result of the product of this number (172) by itself (i.e., 172 × 172); the square of 172 is sometimes called "raising 172 to the power 2", or "172 squared".

The square of 172 is 29 584 because 172 × 172 = 1722 = 29 584.

As a consequence, 172 is the square root of 29 584.

## Number of digits of 172

172 is a number with 3 digits.

## What are the multiples of 172?

The multiples of 172 are all integers evenly divisible by 172, that is all numbers such that the remainder of the division by 172 is zero. There are infinitely many multiples of 172. The smallest multiples of 172 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 172 too, since 0 × 172 = 0
• 172: indeed, 172 is a multiple of itself, since 172 is evenly divisible by 172 (we have 172 / 172 = 1, so the remainder of this division is indeed zero)
• 344: indeed, 344 = 172 × 2
• 516: indeed, 516 = 172 × 3
• 688: indeed, 688 = 172 × 4
• 860: indeed, 860 = 172 × 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 172). 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 13.115). 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 172

• Preceding numbers: …170, 171
• Following numbers: 173, 174

## Nearest numbers from 172

• Preceding prime number: 167
• Following prime number: 173
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