40 (number)

40 (forty) is the natural number following 39 and preceding 41. In English, forty is the only number whose constituent letters appear in alphabetical order.


Cardinal	40 forty
Ordinal	40th fortieth
Numeral system
Factorization	$2^3 \cdot 5$
Divisors	2, 4, 5, 8, 10, 20
Roman numeral	XL
Binary	101000
Hexadecimal	28

In mathematics

Forty is an octagonal number, and as the sum of the first four pentagonal numbers, it is a pentagonal pyramidal number. It is a Harshad 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.

40 is a repdigit in base 3 (1111).

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

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 and Islamic traditions.

"Forty days and forty nights" describes the period for which rain fell during Noah's flood
According to the Midrash, Moses spent three consecutive periods of "forty days and forty nights" on Mount Sinai:

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 worshipping the Golden Calf and broke the tablets
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
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

Rabbi Akiva, the greatest expositor of the Oral Torah, only began learning how to read Hebrew when he was 40 years old
A mikvah consists of 40 se'ah (approximately 200 gallons) of water
"Forty days and forty nights" was the period Jesus spent in the wilderness.
In modern Western Christian practice, Lent consists of the 40 days preceding Easter.
The dead are usually mourned for forty days in Muslim cultures
Some Russians believe that ghosts of the dead linger at the site of their death for forty days

In other fields

Forty is also:

in the maxim "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 800-mile highway that runs from Baltimore, Maryland, to Vandalia, Illinois, being synonymous with the National Highway
- 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
the title of a song by U2
"40 Feet" is the title of a song by Franz Ferdinand
The band Crush 40
in the title of the Food Network show a Day" target="_blank" >^*
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 size used for liquor, typically fairly cheap malt beer; a person sometimes "pours a forty on the curb", i.e., pours out said bottle onto the street, in memory of a person who has died
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 number of hours in a regular workweek in Western countries
the classic Russian vodka is alcohol content 40 percent by volume
the jersey number of Pat Tillman, which was retired by the Arizona Cardinals
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
UB40 is a form for those claiming unemployment benefits in the United Kingdom. The band UB40 was named after this form
the year A.D. 40, 40 BC, or (for example) 1940

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In mathematics

In science

Astronomy

In religion

In other fields

See also