# 135 (number)

 ← 134 135 136 →
Cardinal one hundred thirty-five
Ordinal 135th
(one hundred and thirty-fifth)
Factorization 33× 5
Divisors 1, 3, 5, 9, 15, 27, 45, 135
Roman numeral CXXXV
Binary 100001112
Ternary 120003
Quaternary 20134
Quinary 10205
Senary 3436
Octal 2078
Duodecimal B312
Vigesimal 6F20
Base 36 3R36

135 (one hundred [and] thirty-five) is the natural number following 134 and preceding 136.

## In mathematics

This number in base 10 can be expressed in operations using its own digits in at least two different ways. One is as a sum-product number,

$135 = (1 + 3 + 5)(1 \times 3 \times 5)$

(1 and 144 share this property) and the other is as the sum of consecutive powers of its digits:

$135 = 1^1 + 3^2 + 5^3$

(175, 518, and 598 also have this property).

135 is a Harshad number, and a repdigit in bases 18 and 26.

There are a total of 135 primes between 1,000 and 2,000.

$135 = 11 n^2 + 11 n + 3$ for $n = 3$. This polynomial plays an essential role in Apéry's proof that $\zeta(2)$ is irrational.