# Forty Two

According to pop culture, 42 is the answer. Answer to what? Answer to life, the universe, and everything.

## Properties

### Factorization

The prime factorization of 42 = 2*3*7. This gives the factors: 1,2,3,6,7,14,21, and 42 itself: six proper divisors for a total of seven divisors. 6 and 7 are 1 apart, and 6 times 7, or 7 times 6, = 42, an identity which can be helpful for students to memorize.

The sum of 42's proper divisors is 54, making 42 an abundant number. This sum is higher than any previous number, so 42 is highly abundant.

The whole numbers 42 is between, 41 and 43, are both prime numbers.

### "Magic" shapes

42 is the sum of the diagonals through the center, the rows, and columns of a magic cube:

### For other bases

1. Because 42 has some small divisors, it ends in a 0 for factorable bases. Because 42 is square free, 42 won't end in two zeroes, just one.

2. In binary, 42 is "101010".
3. In ternary, 42 is "1120".
4. In quaternary, 42 is "222", a repunit!
5. In quinary, 42 is "132".
6. In seximal, 42 is "110". Converting 110 from binary to a large enough base gives the digit 6, the radix of seximal!
7. In septimal, 42 is "60".
8. In octal, 42 is "52".
9. In nonary, 42 is "46".
10. In decimal, 42.
11. In elevenary, 42 is "39".
12. In dozenal, 42 is "36".
13. In baker's dozenal, 42 is "33".
14. In biseptimal, 42 is "40".
15. In triquinary, 42 is "2C". A digit for twelve is required, which is C.
16. In hex, 42 is "2A", where A is for ten.
17. In suboptimal, 42 is "37".
18. In triseximal, 42 is "3B".
19. In untriseximal, 42 is "3F".
20. In vigesimal, 42 is "3J".
21. In triseptimal, 42 is "20".
22. In negabinary, 42 is 1111110
and -42 is 101010.
23. In negaternary, 42 is 12210
and -42 is 2110.
24. In negaquaternary, 42 is 322
and -42 is 1232.
25. In negaquinary, 42 is 222
and -42 is 1443.
26. In negaseximal, 42 is 240
and -42 is 1510.
27. In negaseptimal, 42 is 110
and -42 is 1610.
28. In negoctal, 42 is 132
and -42 is 66.
29. In neganonary, 42 is 156
and -42 is 53.
30. In negadecimal, 42 is 162
and -42 is 58.
31. In negelevenary, 42 is 189
and -42 is 42.
32. In negadozenal, 42 is 196
and -42 is 46.
33. In negabaker's dozenal, 42 is 1X3
and -42 is 4X.
34. In negabiseptimal, 42 is 1B0
and -42 is 30.
35. In negatriquinary, 42 is 1DC
and -42 is 33.
36. In negahex, 42 is 1EA
and -42 is 36.
37. In negasuboptimal, 42 is 1F8
and -42 is 39.
38. In negatriseximal, 42 is 1G6
and -42 is 3C.
39. In neguntriseximal, 42 is 1H4
and -42 is 3F.
40. In negavigesimal, 42 is 1I2
and -42 is 3I.
41. In negatriseptimal, 42 is 1J0
and -42 is 20.

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