Forty Two

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.