### About the Number 1440 (one thousand four hundred forty)

MathBabbler created BAB# 1440 on 7 March 2008. For some reason, he felt he had used the number 1440 from time-to-time. It turns out he was familiar with 1440 because that is the number of minutes in one day.

```   1440 is an even, natural, counting, whole, integer
1440 is composite having prime factors:  2^5 * 3^2 * 5
1440 has lots of factors, which include... 1,2,3,4,5,6,8,9,10
1440 in binary is 10110100000 (even # of 1's makes it evil)
1440 in base-8 is 2640
1440 in base-16 is 0x5a0
1440 in Roman numeral is MCDXL
sqrt(1440) = 37.9473319
ln(1440) = 7.27239839
log(1440) = 3.15836249  (0.53% greater than Pi)
```

There are 1440 minutes per day.

```   60 minutes   24 hours    60 * 24 minutes   1440 minutes
---------- * -------- =  --------------- = ------------
1 hour       1 day         1 day             1 day
```

1440 (base-10) is a Harshad number (i.e. the sum of its digits (9) is a factor of 1440).

Up to this BAB, MathBabbler had ignored categorizing numbers as being deficient, perfect, or abundant. The following definition was copied from NumberGossip.com.

```   "The number 'n' is perfect if the sum of all its positive
divisors except itself is equal to 'n'.  Less than perfect
numbers are called deficient, too perfect -- abundant."
```

1440 is an abundant number.

```   the sum of the divisors of 1440...

1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16
+ 18 + 20 + 24 + 30 + 32 + 36 + 40 + 45 + 48 + 60
+ 72 + 80 + 90 + 96 + 120 + 144 + 160 + 180 + 240
+ 288 + 360 + 480 + 720 > 1440

Note:  Suming the largest divisors first we can quickly
see 1440 is abundant: 720 + 480 + 360 = 1560
```

1440 has `1^2, 2^2, 3^2, 4^2, 6^2, 12^2` as divisors.

##### Update::2009.04.02

MathBabbler was doing something with the square-number 1444 and he noticed that this nBAB for the number `1440` was created prior to the creation of the MBNA.

```   MathBabbler Number Analyst (MBNA) output:
=========================================
1440 is a natural, whole, integer
1440 is even
1440 proper divisors are: 1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,
30,32,36,40,45,48,60,72,80,90,96,120,
144,160,180,240,288,360,480,720,
1440 is refactorable (evenly divisable by # of divisors)
1440 is abundant (sum of divisors is 3474)
1440 is unhappy
1440 is a Harshad number
1440 is not prime
1440 has the prime factors: 2*2*2*2*2*3*3*5
1440 sum prime factors: 2...2...2...2...2...3...3...5...answer: 21
1440 in octal is 02640
1440 in hexadecimal is 0x5a0
1440 in binary is 10110100000 (is evil)
1440 nearest square numbers: -71...4 (1369...1444 )
sqrt(1440) = 37.9473
ln(1440) = 7.2724
log(1440) = 3.15836
1440 reciprocal is .00069444444444444444444444444444
1440! is 4.32744e+3924
1440 is 458.366 Pi years
1440 is 72 scoreyears
1440 written as a Roman numeral is MCDXL
```

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 07 March 2008 