Is 169 a prime number? What are the divisors of 169?

Is 169 a prime number?

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

For 169, the answer is: No, 169 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 169) is as follows: 1, 13, 169.

To be 169 a prime number, it would have been required that 169 has only two divisors, i.e., itself and 1.

As a consequence:

  • 169 is a multiple of 1
  • 169 is a multiple of 13

To be 169 a prime number, it would have been required that 169 has only two divisors, i.e., itself and 1.

However, 169 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 169 = 13 x 13, where 13 is a prime number.

Is 169 a deficient number?

Yes, 169 is a deficient number, that is to say 169 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 169 without 169 itself (that is 1 + 13 = 14).

Parity of 169

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

Is 169 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 169 is 13.

Therefore, the square root of 169 is an integer, and as a consequence 169 is a perfect square.

As a consequence, 13 is the square root of 169.

What is the square number of 169?

The square of a number (here 169) is the result of the product of this number (169) by itself (i.e., 169 × 169); the square of 169 is sometimes called "raising 169 to the power 2", or "169 squared".

The square of 169 is 28 561 because 169 × 169 = 1692 = 28 561.

As a consequence, 169 is the square root of 28 561.

Number of digits of 169

169 is a number with 3 digits.

What are the multiples of 169?

The multiples of 169 are all integers evenly divisible by 169, that is all numbers such that the remainder of the division by 169 is zero. There are infinitely many multiples of 169. The smallest multiples of 169 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 169 too, since 0 × 169 = 0
  • 169: indeed, 169 is a multiple of itself, since 169 is evenly divisible by 169 (we have 169 / 169 = 1, so the remainder of this division is indeed zero)
  • 338: indeed, 338 = 169 × 2
  • 507: indeed, 507 = 169 × 3
  • 676: indeed, 676 = 169 × 4
  • 845: indeed, 845 = 169 × 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 169). 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 13). 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 169

  • Preceding numbers: …167, 168
  • Following numbers: 170, 171

Nearest numbers from 169

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