63 (number)

63 is a natural number between 62 and 64. It is an integer and is written in the standard decimal system with two digits: 6 and 3.

63 is a composite number, meaning it has divisors other than 1 and itself. Its prime factorization is 3 × 3 × 7, which can be written as 3² × 7. All of its divisors are 1, 3, 7, 9, 21, and 63.

Mathematical properties

The sum of the divisors of 63 that are less than itself (1 + 3 + 7 + 9 + 21) is 41, which is less than 63. Therefore, 63 is classified as a deficient number. 63 is also an odd number, since it cannot be divided by 2.

63 is equal to 2⁶ − 1, which is one less than 64. In binary, it is written as 111111—six digits, all of which are 1. For this reason, 63 is the highest value that can be represented using six unsigned binary digits. It is also a Mersenne number, though not a prime, since 6 is not prime.

Sequence and form

63 belongs to the sequence of numbers of the form 2ⁿ − 1 (1, 3, 7, 15, 31, 63, 127...). Numbers in this sequence are known as Mersenne numbers.

General use

Because of its relationship to 2⁶, 63 appears in computer arithmetic, for example as the maximum value for six bits, or as a bitmask (bitmask) with all six bits set. It is also used in year notation (63 CE, 1963) and as a common ordinal.