Is 84 a prime number? What are the divisors of 84?

Parity of 84

84 is an even number, because it is evenly divisible by 2: 84 / 2 = 42.

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Is 84 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 84 is about 9.165.

Thus, the square root of 84 is not an integer, and therefore 84 is not a square number.

What is the square number of 84?

The square of a number (here 84) is the result of the product of this number (84) by itself (i.e., 84 × 84); the square of 84 is sometimes called "raising 84 to the power 2", or "84 squared".

The square of 84 is 7 056 because 84 × 84 = 842 = 7 056.

As a consequence, 84 is the square root of 7 056.

Number of digits of 84

84 is a number with 2 digits.

What are the multiples of 84?

The multiples of 84 are all integers evenly divisible by 84, that is all numbers such that the remainder of the division by 84 is zero. There are infinitely many multiples of 84. The smallest multiples of 84 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 84 too, since 0 × 84 = 0
  • 84: indeed, 84 is a multiple of itself, since 84 is evenly divisible by 84 (we have 84 / 84 = 1, so the remainder of this division is indeed zero)
  • 168: indeed, 168 = 84 × 2
  • 252: indeed, 252 = 84 × 3
  • 336: indeed, 336 = 84 × 4
  • 420: indeed, 420 = 84 × 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 84). 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 9.165). 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 84

  • Preceding numbers: …82, 83
  • Following numbers: 85, 86…

Nearest numbers from 84

  • Preceding prime number: 83
  • Following prime number: 89
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