64 (number)

64 is a natural number that lies between 63 and 65. It is composed of two digits: 6 and 4. In the Hindu-Arabic numeral system used worldwide, 64 is written as sixty-four.

The most notable property of 64 is that it is a power of two: it equals 2 multiplied by itself six times (2⁶ = 64). It is also a perfect square (8 × 8 = 64) and a perfect cube (4 × 4 × 4 = 64). For this reason, 64 is one of the few small numbers that is simultaneously a perfect square and a perfect cube, expressed as 2⁶ = (2³)² = (2²)³.

Mathematical properties

The divisors of 64 are 1, 2, 4, 8, 16, 32, and 64—all powers of two. Because it has seven divisors, 64 is not prime; it is a composite number. The sum of its proper divisors (1+2+4+8+16+32 = 63) is less than 64 itself, making it a deficient number.

64 is also the square root of 8 and the cube root of 4. When written in binary notation, it becomes 1000000—a single 1 followed by six zeros, which shows that it is a pure power of two.

Use in computing

Because of 2⁶, the number 64 is used consistently in computer technology. The term '64-bit systems' refers to processors and operating systems that operate on 64-bit units. Base64 is also a method for converting binary data into 64 characters of text so it can be transmitted over text-based networks. Memory and storage measurements commonly follow powers of two, so 64 appears frequently.

Other uses

The chessboard has 64 squares (8 × 8). Other board games such as draughts use the same configuration in some variants. In discrete mathematics, 64 appears in grid graphs that are 8 × 8.