# 144 (number)

144 (number)
144
Cardinal one hundred [and] forty-four
Ordinal 144th
(one hundred [and] forty-fourth)
Factorization $2^4 \cdot 3^2$
Divisors 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Roman numeral CXLIV
Binary 100100002
Octal 2208
Duodecimal 10012

144 is the natural number following 143 and preceding 145. 144 is a dozen dozens, or one gross.

## In mathematics

It is the twelfth Fibonacci number, and the largest one to also be a square, as the square of 12 (which is also its index in the Fibonacci sequence), following 89 and preceding 233.

144 is the smallest number with exactly 15 divisors.

144 is a number that is divisible by the value of its φ function, which returns 48 in this case. Also, there are 21 solutions to the equation φ(x) = 144, more than any integer below 144, making it a highly totient number.

1445 = 275 + 845 + 1105 + 1335, the smallest number whose fifth power is a sum of four (smaller) fifth powers. This solution was found in 1966 by L. J. Lander and T. R. Parkin, and disproved Euler's sum of powers conjecture.

The maximum determinant in a 9 by 9 matrix of zeroes and ones is 144.

144 is in base 10 a sum-product number, as well as a Harshad number.

## In other fields

144 is also:

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