36 (number)
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36 is a natural number lying between 35 and 37. It is a composite number, meaning it has divisors other than 1 and itself.
36 has notable mathematical properties: it is a perfect square (6 × 6 = 36) and a triangular number. It is thus among the small numbers that possess both properties.
Mathematical properties
The prime factorization of 36 is 2² × 3². Its divisors are 1, 2, 3, 4, 6, 9, 12, 18, and 36—nine divisors in total. The sum of its proper divisors (1+2+3+4+6+9+12+18 = 55) exceeds 36 itself, making it an abundant number.
36 is the square of 6 and the eighth triangular number (1+2+3+4+5+6+7+8 = 36). It also equals the sum of the first three cubes: 1³+2³+3³ = 36. This illustrates a relationship between the sum of cubes and the squares of triangular numbers.
Use in measurement and systems
Because 36 is divisible by many numbers (2, 3, 4, 6, 9, 12, 18), it is used in measurement and division systems. For example, a circle of 360 degrees is ten times 36, which facilitates angle division. A group of 36 units can also be easily divided into equal subgroups.
Representation in numeral systems
In base 10, 36 is written as 36. In binary it is 100100. In hexadecimal it is 24. 36 is also used in base-36 representation, which employs the ten digits 0–9 and twenty-six letters to express numbers compactly.