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 [38])
   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

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 United States License.