Is 63 A Prime Number?

Is 63 a prime number? What are the divisors of 63? To content

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

For 63, the answer is: No, 63 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 63) is as follows: 1, 3, 7, 9, 21, 63.

For 63 to be a prime number, it would have been required that 63 has only two divisors, i.e., itself and 1.

Find out more:

• What is a prime number?

As a consequence:

• 63 is a multiple of 1
• 63 is a multiple of 3
• 63 is a multiple of 7
• 63 is a multiple of 9
• 63 is a multiple of 21

For 63 to be a prime number, it would have been required that 63 has only two divisors, i.e., itself and 1.

Is 63 a deficient number?

Yes, 63 is a deficient number, that is to say 63 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 63 without 63 itself (that is 1 + 3 + 7 + 9 + 21 = 41).

63 is an odd number, because it is not evenly divisible by 2.

Find out more:

• What is an even 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 63 is about 7.937.

Thus, the square root of 63 is not an integer, and therefore 63 is not a square number.

The square of a number (here 63) is the result of the product of this number (63) by itself (i.e., 63 × 63); the square of 63 is sometimes called "raising 63 to the power 2", or "63 squared".

The square of 63 is 3 969 because 63 × 63 = 632 = 3 969.

As a consequence, 63 is the square root of 3 969.

63 is a number with 2 digits.

The multiples of 63 are all integers evenly divisible by 63, that is all numbers such that the remainder of the division by 63 is zero. There are infinitely many multiples of 63. The smallest multiples of 63 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 63 too, since 0 × 63 = 0
• 63: indeed, 63 is a multiple of itself, since 63 is evenly divisible by 63 (we have 63 / 63 = 1, so the remainder of this division is indeed zero)
• 126: indeed, 126 = 63 × 2
• 189: indeed, 189 = 63 × 3
• 252: indeed, 252 = 63 × 4
• 315: indeed, 315 = 63 × 5
• etc.

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 63). 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 7.937). 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.

• Preceding numbers: …61, 62
• Following numbers: 64, 65…

Nearest numbers from 63

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

Find out whether some integer is a prime number

Is this number a prime number?

Find out

• Home
• What is a prime number?
• A list of prime numbers
• What is an even number?
• What is a multiple of 3?
• What is a multiple of 5?
• Contact

• Is 0 a prime number?
• Is 1 a prime number?
• Is 2 a prime number?
• Is 2026 a prime number?
• Is 2027 a prime number?
• Is 1133 a prime number?

• Five thousand prime numbers

• Contact

• Est-ce que 63 est un nombre premier ?

• ¿63 es un número primo?