Is 402 a prime number? What are the divisors of 402?

Is 402 a prime number?

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

For 402, the answer is: No, 402 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 402) is as follows: 1, 2, 3, 6, 67, 134, 201, 402.

To be 402 a prime number, it would have been required that 402 has only two divisors, i.e., itself and 1.

As a consequence:

  • 402 is a multiple of 1
  • 402 is a multiple of 2
  • 402 is a multiple of 3
  • 402 is a multiple of 6
  • 402 is a multiple of 67
  • 402 is a multiple of 134
  • 402 is a multiple of 201

To be 402 a prime number, it would have been required that 402 has only two divisors, i.e., itself and 1.

Is 402 a deficient number?

No, 402 is not a deficient number: to be deficient, 402 should have been such that 402 is larger than the sum of its proper divisors, i.e., the divisors of 402 without 402 itself (that is 1 + 2 + 3 + 6 + 67 + 134 + 201 = 414).

In fact, 402 is an abundant number; 402 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 67 + 134 + 201 = 414). The smallest abundant number is 12.

Parity of 402

402 is an even number, because it is evenly divisible by 2: 402 / 2 = 201.

Is 402 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 402 is about 20.050.

Thus, the square root of 402 is not an integer, and therefore 402 is not a square number.

What is the square number of 402?

The square of a number (here 402) is the result of the product of this number (402) by itself (i.e., 402 × 402); the square of 402 is sometimes called "raising 402 to the power 2", or "402 squared".

The square of 402 is 161 604 because 402 × 402 = 4022 = 161 604.

As a consequence, 402 is the square root of 161 604.

Number of digits of 402

402 is a number with 3 digits.

What are the multiples of 402?

The multiples of 402 are all integers evenly divisible by 402, that is all numbers such that the remainder of the division by 402 is zero. There are infinitely many multiples of 402. The smallest multiples of 402 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 402 too, since 0 × 402 = 0
  • 402: indeed, 402 is a multiple of itself, since 402 is evenly divisible by 402 (we have 402 / 402 = 1, so the remainder of this division is indeed zero)
  • 804: indeed, 804 = 402 × 2
  • 1 206: indeed, 1 206 = 402 × 3
  • 1 608: indeed, 1 608 = 402 × 4
  • 2 010: indeed, 2 010 = 402 × 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 402). 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 20.050). 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 402

  • Preceding numbers: …400, 401
  • Following numbers: 403, 404

Nearest numbers from 402

  • Preceding prime number: 401
  • Following prime number: 409
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