40 (number)

← 39 40 41 →
← 40 41 42 43 44 45 46 47 48 49 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	forty
Ordinal	th
Numeral system	quadragesimal
Factorization	$2^{3}\cdot 5$
Divisors	1, 2, 4, 5, 8, 10, 20, 40
Greek numeral	Μ´
Roman numeral	XL
Binary	1010002
Ternary	11113
Senary	1046
Octal	508
Duodecimal	3412
Hexadecimal	2816

40 (forty) is the natural number following 39 and preceding 41.

Despite being related to the word "four" (4), 40 is spelled "forty", not "fourty". This is because etymologically (and still in accents without the horse-hoarse merger), the words have different vowels, "forty" containing a contraction in the same way that "fifty" contains a contraction of "five". The letters of the word "forty" are in alphabetical order; this is the only number that has this linguistic property in English.

In mathematics

Forty is an octagonal number, and as the sum of the first four pentagonal numbers, it is a pentagonal pyramidal number. Adding up some subsets of its divisors (e.g., 1, 4, 5, 10 and 20) gives 40, hence 40 is a semiperfect number.

Given 40, the Mertens function returns 0. 40 is the smallest number n with exactly 9 solutions to the equation φ(x) = n.

Forty is the number of n-queens problem solutions for n = 7.

Since the greatest prime factor of 40² + 1 = 1601 is prime and obviously more than 40 twice, 40 is a Størmer number.

40 is a repdigit in base 3 (1111) and a Harshad number in base 10.

In science

• The atomic number of zirconium.
• Negative forty is the temperature at which the Fahrenheit and Celsius scales correspond; that is, −40°F = −40°C. It is referred to as either "minus forty" or "forty below".

Astronomy

• The planet Venus forms a pentagram in the night sky every eight years with it returning to its original point every 40 years with a 40 day regression (some scholars believe that this ancient information was the basis for the #40 becoming sacred to Jews, Christians, and Muslims).
• Messier object M40, a magnitude 9.0 double star in the constellation Ursa Major
• The New General Catalogue object NGC 40, a magnitude 12.4 planetary nebula in the constellation Cepheus
• The Saros number of the
  • solar eclipse series which began on -1653 May 28 and ended on -373 July 4. The duration of Saros series 40 was 1280.1 years, and it contained 72 solar eclipses.
  • lunar eclipse series which began on -1387 February 12 and ended on -71 April 12. The duration of Saros series 40 was 1316.2 years, and it contained 74 lunar eclipses.

In religion

The number 40 is significant in Jewish, Christian, Islamic, and other Middle Eastern traditions. It can represent an estimate, or many of something.

• Rain fell for "Forty days and forty nights" during Noah's flood
• Spies explored the Promised Land for "Forty days." (Numbers 13)
• Israel wandered in the wilderness for "Forty years". This period of years represents the time it takes for a new generation to arise.
• Moses' life is divided into three 40-year segments, separated by his fleeing from Egypt, and his return to lead his people out.
• Several Israelite leaders and kings are said to have ruled for "forty years", that is, a generation. (Examples: Eli, Saul, David, Solomon.)
• Moses spent three consecutive periods of "forty days and forty nights" on Mount Sinai:

1. He went up on the seventh day of Sivan, after God gave the Torah to the Jewish people, in order to learn the Torah from God, and came down on the seventeenth day of Tammuz, when he saw the Jews worshiping the Golden Calf and broke the tablets
2. He went up on the eighteenth day of Tammuz to beg forgiveness for the people's sin and came down without God's atonement on the twenty-ninth day of Av
3. He went up on the first day of Elul and came down on the tenth day of Tishrei, the first Yom Kippur, with God's atonement

• A mikvah consists of 40 se'ah (approximately 200 gallons) of water
• 40 lashes is one of the punishments meted out by the Sanhedrin, though in actual practice only 39 lashes were administered.
• Jesus was presented at the Temple forty days after his birth.
• Before the temptation of Christ, Jesus fasted "Forty days and forty nights" in the wilderness.
• Forty days was the period from the resurrection of Jesus to the ascension of Jesus.
• In modern Christian practice, Lent consists of the 40 days preceding Easter. In much of Western Christianity Sundays are excluded from the count; in Eastern Christianity Sundays are included.
• The dead are usually mourned for forty days in Muslim cultures.
• Masih ad-Dajjal roams around the Earth in forty days, a period of time that can be as many as forty months, forty years, and so on.
• Khadijah was forty years old when she married Muhammad.
• Muhammad was forty years old when he first received the revelation delivered by the archangel Gabriel.
• The Quran says that a person is only fully grown when they reach the age of 40.
• In the Yazidi faith, The Chermera temple (meaning “40 Men” in the Yazidi dialect) is so old that no one remembers how it came to have that name but it is believed to derive from the burial of 40 men on the mountaintop site.
• Some Russians believe that ghosts of the dead linger at the site of their death for forty days.
• In Hinduism, some popular religious prayers consist of forty shlokas or dohas (couplets, stanzas). The most common being the Hanuman Chalisa (chaalis is the Hindi term for 40).

In other fields

Forty is also:

• The Los Angeles Lakers beat the Houston Rockets by a margin of 40 points in game 5 of the 2008-2009 Playoffs.
• To understand a people, you must live among them for 40 days. ~Arabic proverb
• the caliber of the bullet in the .40 S&W handgun cartridge
• in the Saying "Life begins at forty"
• in the expression "forty winks", meaning a short sleep
• the distance run in the 40 yard dash in American football scouting
• A song by Dave Matthews Band
• the number of years of marriage as the ruby wedding anniversary
• the code for direct dial international phone calls to Romania
• the number in the designation of:
  • Interstate 40, a freeway that runs from California to North Carolina
  • U.S. Route 40, the 2,285-mile (3,677 km) highway that runs from Baltimore, Maryland, to Park City, Utah, a portion of which follows the National Road
  • European route E40 from Calais to Ridder
  • the A40 and M40, important highways in the UK. The A40 is a trunk road in England and Wales, connecting London to Fishguard. The M40 motorway is the second motorway in the British transport network to connect London to Birmingham
• "40", a 1983 song by U2 from their album War
• "40'" is the title of a song by Franz Ferdinand
• The band Crush 40
• in the title of the Food Network show $40 a Day
• in the name of WD-40, a spray lubricant
• in the name of the food additive FD & C Red Dye #40, commonly known as Red 40;
• the 40 ounce (1.183 liter) size used for liquor, a term commonly referred to in Canada
• the number of questions asked in the theory road test in the Republic of Ireland
• the number of thieves in Ali Baba and the Forty Thieves, from Thousand and One Nights (both the numbers 40 and 1001 are more likely to mean "many" than to indicate a specific number)
• the customary number of hours in a regular workweek in some Western countries. The song, "40 Hour Week (For a Livin')" by Alabama (as well as their album, 40-Hour Week), takes its name from the standard workweek length.
• many distilled alcoholic beverages (such as vodka) contain approximately 40 percent alcohol by volume
• the jersey number of Pat Tillman, which was retired by the Arizona Cardinals
• the jersey number of Gayle Sayers, which was retired by the Chicago Bears
• the number of wires in a Parallel ATA-cable
• Form 1040 (referred to as a "ten-forty") is a standard Internal Revenue Service form used to file for federal taxes in the United Sates
• UB40 is a form for those claiming unemployment benefits in the United Kingdom. The band UB40 was named after this form;
• The Rolling Stones CD Forty Licks;
• the number of positions on a number of radio countdown programs, most notably American Top 40 and American Country Countdown.
• for The Early Show segment "Chef on a Shoestring", chefs are given a $40 budget. Most chefs bring it in under. (For holidays they are given $80).
• the M40 (field protective mask), a United States military gas mask
• generally considered the number of points that a Premier League team needs to avoid relegation.
• forty is the number of weeks for an average term of pregnancy, counting from the woman’s last menstrual period.
• The age for people is middle age in some cultures.
• The number of the French department Landes
• In tennis, the number 40 represents the third point gained in a game. A score of 40-40 (three points each) is called "deuce", at which time a player must score two consecutive points to win the game.
• Ronald Reagan was the 40th president of the United States;
• In the song "Billie Jean" by Michael Jackson, the lyrics state that "For forty days and for forty nights / the law was on her side" in reference to the Genesis story of Noah.

Historical years

40 A.D., 40 B.C., 1940, 2040, etc.

See also

• 40 acres and a mule