# 40 (number)

 ← 39 40 41 →
Cardinalforty
Ordinal40th
(fortieth)
Factorization23· 5
Divisors1, 2, 4, 5, 8, 10, 20, 40
Roman numeralXL
Binary1010002
Ternary11113
Quaternary2204
Quinary1305
Senary1046
Octal508
Duodecimal3412
Vigesimal2020
Base 361436

 ← 39 40 41 →
Cardinalforty
Ordinal40th
(fortieth)
Factorization23· 5
Divisors1, 2, 4, 5, 8, 10, 20, 40
Roman numeralXL
Binary1010002
Ternary11113
Quaternary2204
Quinary1305
Senary1046
Octal508
Duodecimal3412
Vigesimal2020
Base 361436

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

Despite being related to the word "four" (4), 40 is spelled "forty", and not "fourty". The reason is that etymologically (also in accents without the horse–hoarse merger),[citation needed] the words have different vowels, "forty" containing a contraction in the same way that "fifty" contains a contraction of "five".

## In mathematics

Forty is a composite number, 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 402 + 1 = 1601 is prime, 40 is a Størmer number.

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

40 and "The Rule of Three" - If you have a topic which is broken down into three sections,each of these is broken down into three sub-sections and each of these three sub-sections is broken down into a further three sections (three generations using the "rule of three") gives you a total of 40 sections (1+3+9+27).

## In science

• The atomic number of zirconium.
• Negative forty is the unique 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".

## In religion

The number 40 is used in Jewish, Christian, Islamic, and other Middle Eastern traditions to represent a large, approximate number, similar to "umpteen".

### Judaism

In the Hebrew Bible, forty is often used for time periods, forty days or forty years, which separate "two distinct epochs".[1]

• Rain fell for "forty days and forty nights" during the Flood
• Spies explored the land of Israel for "forty days." (Numbers 13)
• The Hebrew people lived in the Sinai desert 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 Jewish leaders and kings are said to have ruled for "forty years", that is, a generation. (Examples: Eli, Saul, David, Solomon.)
• Goliath challenged the Israelites twice a day for forty days before David defeated him.
• 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.[citation needed]
• One of the prerequisites for a man to study Kabbalah is that he is forty years old.

### Christianity

Christianity similarly uses forty to designate important time periods.[1]

### Islam

• Muhammad was forty years old when he first received the revelation delivered by the archangel Gabriel.
• 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.
• Allah forbade the Fasiqun (the non-believers) from entering the Holy Land for 40 years to separate them from Musa (Moses) and his brother.[2]
• Musa (Moses) spent 40 days on Mount Sinai where he received the 10 commandments.[3]
• Prophet Ibrahim spent 40 days in a fire and lived because Allah made the fire like flowers.[citation needed]
• On the 40th verse (ayat) of the 2nd chapter of the Quran (Al-Baqarah) Allah changes the topic.
• Forty was the number of days that Prophet Ilyas (Elijah) spent in the wilderness before the angel appeared to him with Allah's message on Mount Horeb.[citation needed]
• Forty was the number of days that Prophet Isa (Jesus) was tempted in the desert by Satan.[citation needed]
• Muhammad praying and fasting in the cave for 40 days.[citation needed]
• Prophets Dawuud and Suleiman each ruled for forty years.[citation needed]
• Regarding the flood that Noah encountered, it is said that for forty days water continued to pour from the heavens and to stream out over the earth.[citation needed]
• There is also a hadith from Mohammad that the prayers of a person who gossips would not be accepted for forty days and nights. (Al-Kafi, Vol. 6, p. 400)
• Imam Ali has narrated from Mohammad that one who memorizes and preserves forty hadith relating to their religious needs shall be raised by Allah as a learned scholar on the Day of Resurrection.[citation needed]
• It is said that a person’s intellect attains maturity in forty years, everyone according to his own capacity.[4]
• It is believed that one who assists a blind man for forty steps becomes worthy of entering heaven.[citation needed]
• Imam Baghir has said: “The prayers of someone who drinks wine are not accepted for forty days.”[citation needed]
• Believers have also been encouraged to devote themselves to God Almighty for forty days to see the springs of wisdom break forth from their hearts and flow from their tongues.[citation needed]
• Mourning period officially last for 40 days.[citation needed]
• Arba'een (meaning "40") is a Shia Muslim religious observance that occurs 40 days after the Day of Ashura.

### Yazidism

• 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.

### Funerary customs

• Some Russians believe that ghosts of the dead linger at the site of their death for forty days.
• Many Christian Filipinos mark the end of the initial mourning period on the fortieth day after death, and have a Mass said. They believe that the soul remains on the earthly plane for forty days before entering the afterlife, recalling how Christ ascended to heaven forty days after his Resurrection.

### Hinduism

• 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 Hindu system some of the popular fasting period consist 40 days and is called the period One 'Mandl kal' Kal means a period and Mandal kal means a period of 40 days. For example the devotees of 'Swami Ayyappa', the name of a Hindu God very popular in Kerala, India ( Sabarimala Swami Ayyappan ) strictly observed forty days fasting and visit ( Only male devotees are permitted to enter into the God's Temple) with their holy submittance or offerings on 41st or a convenient day after a minimum 40 days practice of fasting. The offering is called 'Kanikka'.

### Sumerian

• Enki ( /ˈɛŋki/) or Enkil (Sumerian: dEN.KI(G)𒂗𒆠) is a god in Sumerian mythology, later known as Ea in Akkadian and Babylonian mythology. He was originally patron god of the city of Eridu, but later the influence of his cult spread throughout Mesopotamia and to the Canaanites, Hittites and Hurrians. He was the deity of crafts (gašam); mischief; water, seawater, lakewater (a, aba, ab), intelligence (gestú, literally "ear") and creation (Nudimmud: nu, likeness, dim mud, make bear). He was associated with the southern band of constellations called stars of Ea, but also with the constellation AŠ-IKU, the Field (Square of Pegasus).[1] Beginning around the second millennium BCE, he was sometimes referred to in writing by the numeric ideogram for "40," occasionally referred to as his "sacred number."[2][3][4]

A large number of myths about Enki have been collected from many sites, stretching from Southern Iraq to the Levantine coast. He figures in the earliest extant cuneiform inscriptions throughout the region and was prominent from the third millennium down to Hellenistic times.

The exact meaning of his name is uncertain: the common translation is "Lord of the Earth": the Sumerian en is translated as a title equivalent to "lord"; it was originally a title given to the High Priest; ki means "earth"; but there are theories that ki in this name has another origin, possibly kig of unknown meaning, or kur meaning "mound". The name Ea is allegedly Hurrian in origin while others [5][6] claim that it is possibly of Semitic origin and may be a derivation from the West-Semitic root *hyy meaning "life" in this case used for "spring", "running water." In Sumerian E-A means "the house of water", and it has been suggested that this was originally the name for the shrine to the God at Eridu.

## In other fields

The number on the logo for the American-Japanese hard rock band Crush 40 from the Sonic the Hedgehog franchise.

Forty is also: