Is 146 a prime number? What are the divisors of 146?

Is 146 a prime number?

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

For 146, the answer is: No, 146 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 146) is as follows: 1, 2, 73, 146.

To be 146 a prime number, it would have been required that 146 has only two divisors, i.e., itself and 1.

As a consequence:

  • 146 is a multiple of 1
  • 146 is a multiple of 2
  • 146 is a multiple of 73

To be 146 a prime number, it would have been required that 146 has only two divisors, i.e., itself and 1.

However, 146 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 146 = 2 x 73, where 2 and 73 are both prime numbers.

Is 146 a deficient number?

Yes, 146 is a deficient number, that is to say 146 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 146 without 146 itself (that is 1 + 2 + 73 = 76).

Parity of 146

146 is an even number, because it is evenly divisible by 2: 146 / 2 = 73.

Is 146 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 146 is about 12.083.

Thus, the square root of 146 is not an integer, and therefore 146 is not a square number.

What is the square number of 146?

The square of a number (here 146) is the result of the product of this number (146) by itself (i.e., 146 × 146); the square of 146 is sometimes called "raising 146 to the power 2", or "146 squared".

The square of 146 is 21 316 because 146 × 146 = 1462 = 21 316.

As a consequence, 146 is the square root of 21 316.

Number of digits of 146

146 is a number with 3 digits.

What are the multiples of 146?

The multiples of 146 are all integers evenly divisible by 146, that is all numbers such that the remainder of the division by 146 is zero. There are infinitely many multiples of 146. The smallest multiples of 146 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 146 too, since 0 × 146 = 0
  • 146: indeed, 146 is a multiple of itself, since 146 is evenly divisible by 146 (we have 146 / 146 = 1, so the remainder of this division is indeed zero)
  • 292: indeed, 292 = 146 × 2
  • 438: indeed, 438 = 146 × 3
  • 584: indeed, 584 = 146 × 4
  • 730: indeed, 730 = 146 × 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 146). 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 12.083). 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 146

  • Preceding numbers: …144, 145
  • Following numbers: 147, 148

Nearest numbers from 146

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