Is 138 a prime number? What are the divisors of 138?

Parity of 138

138 is an even number, because it is evenly divisible by 2: 138 / 2 = 69.

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Is 138 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 138 is about 11.747.

Thus, the square root of 138 is not an integer, and therefore 138 is not a square number.

What is the square number of 138?

The square of a number (here 138) is the result of the product of this number (138) by itself (i.e., 138 × 138); the square of 138 is sometimes called "raising 138 to the power 2", or "138 squared".

The square of 138 is 19 044 because 138 × 138 = 1382 = 19 044.

As a consequence, 138 is the square root of 19 044.

Number of digits of 138

138 is a number with 3 digits.

What are the multiples of 138?

The multiples of 138 are all integers evenly divisible by 138, that is all numbers such that the remainder of the division by 138 is zero. There are infinitely many multiples of 138. The smallest multiples of 138 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 138 too, since 0 × 138 = 0
  • 138: indeed, 138 is a multiple of itself, since 138 is evenly divisible by 138 (we have 138 / 138 = 1, so the remainder of this division is indeed zero)
  • 276: indeed, 276 = 138 × 2
  • 414: indeed, 414 = 138 × 3
  • 552: indeed, 552 = 138 × 4
  • 690: indeed, 690 = 138 × 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 138). 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 11.747). 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 138

  • Preceding numbers: …136, 137
  • Following numbers: 139, 140…

Nearest numbers from 138

  • Preceding prime number: 137
  • Following prime number: 139
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