# 135 (number)

 ← 134 135 136 →
Cardinal one hundred thirty-five
Ordinal 135th
(one hundred thirty-fifth)
Factorization 33× 5
Divisors 1, 3, 5, 9, 15, 27, 45, 135
Greek numeral ΡΛΕ´
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,

${\displaystyle 135=(1+3+5)(1\times 3\times 5)}$

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

${\displaystyle 135=1^{1}+3^{2}+5^{3}}$

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

135 is a Harshad number,[2] and a repdigit in bases 18 and 26.

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

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