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Quiz about The Answer
Quiz about The Answer

The Answer Trivia Quiz

Mathematical Properties of the Number 42

No number has sparked as much controversy and excitement in nerd culture as 42. Famously known in pop culture as "the answer to life, the universe, and everything," the number 42 also boasts fascinating mathematical properties. Let's take a closer look!

by Matthew_07. Estimated time: 4 mins.
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Author
Matthew_07
Time
4 mins
Type
Quiz #
418,686
Updated
Jan 02 25
# Qns
10
Difficulty
Average
Avg Score
7 / 10
Plays
124
Awards
Editor's Choice
Last 3 plays: DizWiz (10/10), MemeQueen (5/10), Nicobutch (8/10).
The number 42 holds a unique place in mathematics, specifically in the field of number theory, due to its interesting properties.

First, the number 42 ends with 2, making it divisible by 2 and therefore an number. Its factorization is 2 × 3 × 7, making it a number.

Remarkably, 42 is a number as it equals the product of two consecutive integers, namely 6 × 7. It is also a number or panarithmic number, because every positive integer smaller than 42 can be expressed as sum of its divisors: 1, 2, 3, 6, 7, 14, and 21. Additionally, 42 is an number, also known as excessive number, because the sum of its proper divisors is greater than the number itself, as evident in the inequality 1 + 2 + 3 + 6 + 7 + 14 + 21 = 54 > 42.

Furthermore, 42 is a number - a term coined by Indian mathematician D. R. Kaprekar, as it is divisible by the sum of its digits - note that 4 + 2 = 6, and 42 ÷ 6 = 7. Not to be confused with the name of a Romance language, the number 42 is a number, that appears in various combinatorial contexts, such as lattice paths, binary trees, and counting problems.

Beyond these properties, 42 is classified as a primary number. This means that the sum of the reciprocals of its prime divisors and the number itself, equals 1, as in 1/2 + 1/3 + 1/7 + 1/42 = 1. Its representation, 101010, is visually aesthetic, characterized by alternating bits.
Your Options
[binary] [Harshad] [pseudoperfect] [even] [abundant] [prime] [practical] [Catalan] [pronic] [composite]

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Quiz Answer Key and Fun Facts
Answer:

All positive integers ending in 0, 2, 4, 6, or 8 are even numbers and, therefore, divisible by 2.

Prime factorization, also known as integer factorization, is a mathematical process that breaks down a given integer into a product of smaller integers. For example, 42 can be expressed as 2×3×7, which is a product of three prime numbers. This makes 42 a composite number.

Pronic numbers, being the product of two consecutive integers, are always even. The first few pronic numbers are 0, 2, 6, 12, 20, 30, and 42.

The number 42 is the 16th practical number. When Srinivasan introduced the term in 1948, he commented "the subdivisions of money, weights, and measures involve numbers like 4, 12, 16, 20 and 28 which are usually supposed to be so inconvenient as to deserve replacement by powers of 10."

The first few abundant numbers are 12, 18, 20, 24, 30, 36, 40, and 42. It is interesting to note that 945 is the smallest odd abundant number.

The term Harshad, meaning "giving joy" in Sanskrit, was coined by Indian mathematician D. R. Kaprekar (1905 - 1986).

Catalan numbers are named after French mathematician Eugène Charles Catalan (1814 - 1894). The first few Catalan numbers are 1, 1, 2, 5, 14, and 42.

Works on primary pseudoperfect numbers began in 2000, where mathematicians employed rigorous search techniques in search of these elusive integers.

Binary numbers are numbers that are expressed in base 2. The number 101010 in base 2, is equivalent to 1 × 2^5 + 0 × 2^4 + 1 × 2^3 + 0 × 2^2 + 1 × 2^1 + 0 × 2^0 = 42 in base 10.

In "The Hitchhiker's Guide to the Galaxy" (1979), penned by English author Douglas Adams, the number 42 is "the Answer to the Ultimate Question of Life, The Universe, and Everything".

In 1993, Adams provided the following response when he was asked about the choice of the number. "The answer to this is very simple. It was a joke. It had to be a number, an ordinary, smallish number, and I chose that one. Binary representations, base thirteen, Tibetan monks are all complete nonsense. I sat at my desk, stared into the garden and thought '42 will do' I typed it out. End of story."

The next time you roll a pair of dice in a game of Monopoly, try counting the total number of pips on the two dice. The answer? 42!
Source: Author Matthew_07

This quiz was reviewed by FunTrivia editor WesleyCrusher before going online.
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