Is 105 a prime number? What are the divisors of 105?

Is 105 a prime number?

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

For 105, the answer is: No, 105 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 105) is as follows: 1, 3, 5, 7, 15, 21, 35, 105.

To be 105 a prime number, it would have been required that 105 has only two divisors, i.e., itself and 1.

As a consequence:

  • 105 is a multiple of 1
  • 105 is a multiple of 3
  • 105 is a multiple of 5
  • 105 is a multiple of 7
  • 105 is a multiple of 15
  • 105 is a multiple of 21
  • 105 is a multiple of 35

To be 105 a prime number, it would have been required that 105 has only two divisors, i.e., itself and 1.

Is 105 a deficient number?

Yes, 105 is a deficient number, that is to say 105 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 105 without 105 itself (that is 1 + 3 + 5 + 7 + 15 + 21 + 35 = 87).

Parity of 105

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

Is 105 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 105 is about 10.247.

Thus, the square root of 105 is not an integer, and therefore 105 is not a square number.

What is the square number of 105?

The square of a number (here 105) is the result of the product of this number (105) by itself (i.e., 105 × 105); the square of 105 is sometimes called "raising 105 to the power 2", or "105 squared".

The square of 105 is 11 025 because 105 × 105 = 1052 = 11 025.

As a consequence, 105 is the square root of 11 025.

Number of digits of 105

105 is a number with 3 digits.

What are the multiples of 105?

The multiples of 105 are all integers evenly divisible by 105, that is all numbers such that the remainder of the division by 105 is zero. There are infinitely many multiples of 105. The smallest multiples of 105 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 105 too, since 0 × 105 = 0
  • 105: indeed, 105 is a multiple of itself, since 105 is evenly divisible by 105 (we have 105 / 105 = 1, so the remainder of this division is indeed zero)
  • 210: indeed, 210 = 105 × 2
  • 315: indeed, 315 = 105 × 3
  • 420: indeed, 420 = 105 × 4
  • 525: indeed, 525 = 105 × 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 105). 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 10.247). 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 105

  • Preceding numbers: …103, 104
  • Following numbers: 106, 107

Nearest numbers from 105

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