Is 135 a prime number? What are the divisors of 135?

Is 135 a prime number?

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

For 135, the answer is: No, 135 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 135) is as follows: 1, 3, 5, 9, 15, 27, 45, 135.

To be 135 a prime number, it would have been required that 135 has only two divisors, i.e., itself and 1.

As a consequence:

  • 135 is a multiple of 1
  • 135 is a multiple of 3
  • 135 is a multiple of 5
  • 135 is a multiple of 9
  • 135 is a multiple of 15
  • 135 is a multiple of 27
  • 135 is a multiple of 45

To be 135 a prime number, it would have been required that 135 has only two divisors, i.e., itself and 1.

Is 135 a deficient number?

Yes, 135 is a deficient number, that is to say 135 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 135 without 135 itself (that is 1 + 3 + 5 + 9 + 15 + 27 + 45 = 105).

Parity of 135

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

Is 135 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 135 is about 11.619.

Thus, the square root of 135 is not an integer, and therefore 135 is not a square number.

What is the square number of 135?

The square of a number (here 135) is the result of the product of this number (135) by itself (i.e., 135 × 135); the square of 135 is sometimes called "raising 135 to the power 2", or "135 squared".

The square of 135 is 18 225 because 135 × 135 = 1352 = 18 225.

As a consequence, 135 is the square root of 18 225.

Number of digits of 135

135 is a number with 3 digits.

What are the multiples of 135?

The multiples of 135 are all integers evenly divisible by 135, that is all numbers such that the remainder of the division by 135 is zero. There are infinitely many multiples of 135. The smallest multiples of 135 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 135 too, since 0 × 135 = 0
  • 135: indeed, 135 is a multiple of itself, since 135 is evenly divisible by 135 (we have 135 / 135 = 1, so the remainder of this division is indeed zero)
  • 270: indeed, 270 = 135 × 2
  • 405: indeed, 405 = 135 × 3
  • 540: indeed, 540 = 135 × 4
  • 675: indeed, 675 = 135 × 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 135). 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 11.619). 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 135

  • Preceding numbers: …133, 134
  • Following numbers: 136, 137

Nearest numbers from 135

  • Preceding prime number: 131
  • Following prime number: 137
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