135 (number)

135 is a natural number that lies between 134 and 136. It is an odd number, since it cannot be divided evenly by two, and it is a composite number—meaning it has divisors other than 1 and itself.

In the base-ten numeral system, it consists of three digits: one hundred, three tens, and five ones. The sum of its digits is 1 + 3 + 5 = 9.

Mathematical properties

The prime factorization of 135 is 3 × 3 × 3 × 5, which can be written as 3³ × 5. It is therefore the product of 27 and 5. Its divisors are 1, 3, 5, 9, 15, 27, 45, and 135—eight divisors in total.

135 is a Harshad number (also called a Niven number): it is evenly divisible by the sum of its digits, since 135 ÷ 9 = 15. It also has a notable property relating to its digits: 1¹ + 3² + 5³ = 1 + 9 + 125 = 135, making it an example of what are called narcissistic numbers, in which the digits raised to successive powers sum to the original number.

Geometric significance

The number 135 appears in angle measurement: an angle of 135 degrees is an obtuse angle, and it is the complement of a 45-degree angle on a full circle. It is also the interior angle of each vertex of a regular octagon.

Other uses

Like other numbers, 135 serves as a reference number in coding systems used to distinguish categories, such as road designations, house numbers, and page numbering. Its meaning depends on the system being used and has no fixed universal significance.