42 is a Harshad number in base 10, because the sum of the digits 4 and 2 is 6 (4 + 2 = 6), and 42 is divisible by 6.42 is the sum of the first 6 positive even numbers.42 is the smallest number k such that for every Riemann surface C, #Aut( C) ≤ k deg( K C) = k(2 g − 2) ( Hurwitz's automorphisms theorem).42 is the largest number n such that there exist positive integers p, q, r with 1 = 1 / n + 1 / p + 1 / q + 1 / r.
The dimension of the Borel subalgebra in the exceptional Lie algebra e 6 is 42.42 is the resulting number of the original Smith number (4937775 = 3 × 5 × 5 × 65837): Both the sum of its digits (4 + 9 + 3 + 7 + 7 + 7 + 5) and the sum of the digits in its prime factorization (3 + 5 + 5 + (6 + 5 + 8 + 3 + 7)) result in 42.Whether there are other values remains an open question. 42 is the only known value that is the number of sets of four distinct positive integers a, b, c, d, each less than the value itself, such that ab − cd, ac − bd, and ad − bc are each multiples of the value.It is a meandric number and an open meandric number. It is the third pentadecagonal number.Given 27 same-size cubes whose nominal values progress from 1 to 27, a 3 × 3 × 3 magic cube can be constructed such that every row, column, and corridor, and every diagonal passing through the center, is composed of 3 numbers whose sum of values is 42.The 3 × 3 × 3 simple magic cube with rows summing to 42. It is the number of partitions of 10-the number of ways of expressing 10 as a sum of positive integers (note a different sense of partition from that above).It is an alternating sign matrix number, that is, the number of 4-by-4 alternating sign matrices.Consequently, 42 is the number of noncrossing partitions of a set of five elements, the number of triangulations of a heptagon, the number of rooted ordered binary trees with six leaves, the number of ways in which five pairs of nested parentheses can be arranged, etc. It is the third primary pseudoperfect number.The group stage of the FIFA World cup is a good example. In other words, it is the number of all possible outcomes (up to isomorphism) of a tournament consisting of 4 teams where the game between any pair of teams results in three possible outcomes: the first team wins, the second team wins, or there is a draw. It is the number of isomorphism classes of all simple and oriented directed graphs on 4 vertices.3 Īdditional properties of the number 42 include:.7 makes it the second sphenic number and also the second of the form (2.6.1 The Hitchhiker's Guide to the Galaxyįorty-two (42) is a pronic number and an abundant number its prime factorization 2.