Is 64 a prime number? What are the divisors of 64?

Is 64 a prime number?

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

For 64, the answer is: No, 64 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 64) is as follows: 1, 2, 4, 8, 16, 32, 64.

To be 64 a prime number, it would have been required that 64 has only two divisors, i.e., itself and 1.

As a consequence:

  • 64 is a multiple of 1
  • 64 is a multiple of 2
  • 64 is a multiple of 4
  • 64 is a multiple of 8
  • 64 is a multiple of 16
  • 64 is a multiple of 32

To be 64 a prime number, it would have been required that 64 has only two divisors, i.e., itself and 1.

Is 64 a deficient number?

Yes, 64 is a deficient number, that is to say 64 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 64 without 64 itself (that is 1 + 2 + 4 + 8 + 16 + 32 = 63).

Parity of 64

64 is an even number, because it is evenly divisible by 2: 64 / 2 = 32.

Is 64 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 64 is 8.

Therefore, the square root of 64 is an integer, and as a consequence 64 is a perfect square.

As a consequence, 8 is the square root of 64.

What is the square number of 64?

The square of a number (here 64) is the result of the product of this number (64) by itself (i.e., 64 × 64); the square of 64 is sometimes called "raising 64 to the power 2", or "64 squared".

The square of 64 is 4 096 because 64 × 64 = 642 = 4 096.

As a consequence, 64 is the square root of 4 096.

Number of digits of 64

64 is a number with 2 digits.

What are the multiples of 64?

The multiples of 64 are all integers evenly divisible by 64, that is all numbers such that the remainder of the division by 64 is zero. There are infinitely many multiples of 64. The smallest multiples of 64 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 64 too, since 0 × 64 = 0
  • 64: indeed, 64 is a multiple of itself, since 64 is evenly divisible by 64 (we have 64 / 64 = 1, so the remainder of this division is indeed zero)
  • 128: indeed, 128 = 64 × 2
  • 192: indeed, 192 = 64 × 3
  • 256: indeed, 256 = 64 × 4
  • 320: indeed, 320 = 64 × 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 64). 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 8). 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 64

  • Preceding numbers: …62, 63
  • Following numbers: 65, 66

Nearest numbers from 64

  • Preceding prime number: 61
  • Following prime number: 67
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