Is 106 a prime number? What are the divisors of 106?

Is 106 a prime number?

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

For 106, the answer is: No, 106 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 106) is as follows: 1, 2, 53, 106.

To be 106 a prime number, it would have been required that 106 has only two divisors, i.e., itself and 1.

As a consequence:

  • 106 is a multiple of 1
  • 106 is a multiple of 2
  • 106 is a multiple of 53

To be 106 a prime number, it would have been required that 106 has only two divisors, i.e., itself and 1.

However, 106 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 106 = 2 x 53, where 2 and 53 are both prime numbers.

Is 106 a deficient number?

Yes, 106 is a deficient number, that is to say 106 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 106 without 106 itself (that is 1 + 2 + 53 = 56).

Parity of 106

106 is an even number, because it is evenly divisible by 2: 106 / 2 = 53.

Is 106 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 106 is about 10.296.

Thus, the square root of 106 is not an integer, and therefore 106 is not a square number.

What is the square number of 106?

The square of a number (here 106) is the result of the product of this number (106) by itself (i.e., 106 × 106); the square of 106 is sometimes called "raising 106 to the power 2", or "106 squared".

The square of 106 is 11 236 because 106 × 106 = 1062 = 11 236.

As a consequence, 106 is the square root of 11 236.

Number of digits of 106

106 is a number with 3 digits.

What are the multiples of 106?

The multiples of 106 are all integers evenly divisible by 106, that is all numbers such that the remainder of the division by 106 is zero. There are infinitely many multiples of 106. The smallest multiples of 106 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 106 too, since 0 × 106 = 0
  • 106: indeed, 106 is a multiple of itself, since 106 is evenly divisible by 106 (we have 106 / 106 = 1, so the remainder of this division is indeed zero)
  • 212: indeed, 212 = 106 × 2
  • 318: indeed, 318 = 106 × 3
  • 424: indeed, 424 = 106 × 4
  • 530: indeed, 530 = 106 × 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 106). 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 10.296). 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 106

  • Preceding numbers: …104, 105
  • Following numbers: 107, 108

Nearest numbers from 106

  • Preceding prime number: 103
  • Following prime number: 107
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