# 144 (number)

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 ← 143 144 145 →
Cardinal one hundred forty-four
Ordinal 144th
(one hundred and forty-fourth)
Factorization 24× 32
Divisors 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Roman numeral CXLIV
Binary 100100002
Ternary 121003
Quaternary 21004
Quinary 10345
Senary 4006
Octal 2208
Duodecimal 10012
Hexadecimal 9016
Vigesimal 7420
Base 36 4036

144 (one hundred [and] forty-four) is the natural number following 143 and preceding 145. 144 is a dozen dozens, or one gross.

## In mathematics

144 is the twelfth Fibonacci number, and the largest one to also be a square,[1] 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, but it is not highly composite since a smaller number 120 has 16 divisors.

144 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.

$144^5 = 27^5 + 84^5 + 110^5 + 133^5$, 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. 144 is a repdigit in bases 15, 17, 23, 35, 47, 71, and 143.

144 is also:

## References

1. ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 165
2. ^ College Hoops Net
3. ^ Porter, Darwin; Danforth Prince (2009). Frommer's Austria. Hoboken, New Jersey: Frommer's. p. 482. ISBN 978-0-470-39897-5.