Is 144 a prime number? What are the divisors of 144?

Is 144 a prime number?

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

For 144, the answer is: No, 144 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 144) is as follows: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.

To be 144 a prime number, it would have been required that 144 has only two divisors, i.e., itself and 1.

As a consequence:

  • 144 is a multiple of 1
  • 144 is a multiple of 2
  • 144 is a multiple of 3
  • 144 is a multiple of 4
  • 144 is a multiple of 6
  • 144 is a multiple of 8
  • 144 is a multiple of 9
  • 144 is a multiple of 12
  • 144 is a multiple of 16
  • 144 is a multiple of 18
  • 144 is a multiple of 24
  • 144 is a multiple of 36
  • 144 is a multiple of 48
  • 144 is a multiple of 72

To be 144 a prime number, it would have been required that 144 has only two divisors, i.e., itself and 1.

Is 144 a deficient number?

No, 144 is not a deficient number: to be deficient, 144 should have been such that 144 is larger than the sum of its proper divisors, i.e., the divisors of 144 without 144 itself (that is 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 36 + 48 + 72 = 259).

In fact, 144 is an abundant number; 144 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 36 + 48 + 72 = 259). The smallest abundant number is 12.

Parity of 144

144 is an even number, because it is evenly divisible by 2: 144 / 2 = 72.

Is 144 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 144 is 12.

Therefore, the square root of 144 is an integer, and as a consequence 144 is a perfect square.

As a consequence, 12 is the square root of 144.

What is the square number of 144?

The square of a number (here 144) is the result of the product of this number (144) by itself (i.e., 144 × 144); the square of 144 is sometimes called "raising 144 to the power 2", or "144 squared".

The square of 144 is 20 736 because 144 × 144 = 1442 = 20 736.

As a consequence, 144 is the square root of 20 736.

Number of digits of 144

144 is a number with 3 digits.

What are the multiples of 144?

The multiples of 144 are all integers evenly divisible by 144, that is all numbers such that the remainder of the division by 144 is zero. There are infinitely many multiples of 144. The smallest multiples of 144 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 144 too, since 0 × 144 = 0
  • 144: indeed, 144 is a multiple of itself, since 144 is evenly divisible by 144 (we have 144 / 144 = 1, so the remainder of this division is indeed zero)
  • 288: indeed, 288 = 144 × 2
  • 432: indeed, 432 = 144 × 3
  • 576: indeed, 576 = 144 × 4
  • 720: indeed, 720 = 144 × 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 144). 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 12). 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 144

  • Preceding numbers: …142, 143
  • Following numbers: 145, 146

Nearest numbers from 144

  • Preceding prime number: 139
  • Following prime number: 149
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