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|Factorization||7 × 11|
|Divisors||1, 7, 11, 77|
77 has an aliquot sum of 19 and it is the second number to do so the first being 65; 77 is the 2nd member of the 19-aliquot tree.
It is the sum of three squares, 42 + 52 + 62, as well as the sum of the first eight prime numbers.
It is the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1.
77 and 78 form a Ruth–Aaron pair.
It and its sibling 49 are the only 2-digit numbers whose home primes (in base 10) have not been calculated.
During World War II in Sweden at the border with Norway, "77" was used as a shibboleth (password), because the tricky pronunciation in Swedish made it easy to instantly discern whether the speaker was native Swedish, Norwegian, or German.
In the Islamic tradition, "77" figures prominently. Muhammad is reported to have explained, "Faith has sixty-odd, or seventy-odd branches, the highest and best of which is to declare that there is no god but God, and the lowest of which is to remove something harmful from a road. Shyness, too, is a branch of faith." While some scholars refrain from clarifying "sixty-odd or seventy-odd", various numbers have been suggested, 77 being the most common. Some have gone so far as to delineate these branches.
In religious numerology
In certain numerological systems based on the English alphabet, the number 77 is associated with Jesus Christ. CHRIST is C = 3, H = 8, R = 18, I = 9, S = 19, T = 20, which added together equal 77.
'Liber 77' is the gematrian name for Liber OZ- a brief but popular publication by Aliester Crowley. The word 'oz', which means 'strength', is composed of two hebrew letters- ayin and zayin, which have gematrian values of 70 and 7 respectively, thus adding up to 77.
- Portland Trail Blazers coach Jack Ramsay led his team to their only NBA title in his first season. #77 was retired in honor of the 1977 NBA title.
- The number posthumously retired by the Minnesota Vikings of the NFL for offensive lineman Korey Stringer.
- The number worn by Ray Bourque in the NHL from 1987 to 2001. This number has been retired by the Boston Bruins, with whom he played for 20 years, and the Colorado Avalanche, with whom he won the Stanley Cup in his last NHL game. He wore 77 after his previous number (7), which he wore for his first eight seasons, was retired for Phil Esposito.
- The number worn by football legend Red Grange. Retired by both the University of Illinois and the Chicago Bears.
- The number worn by NFL Hall of Famer Jim Parker. Retired by the Indianapolis Colts
- The number worn by NFL offensive tackle Stan Mauldin. Retired by the Arizona Cardinals.
- The number worn by NCAA football legend Dennis Byrd. Retired by NC State in 2001.
- The number worn by NCAA football legend John Schmitt. Retired by Hofstra University.
- The number worn by Alex Melvin of the Pickering Red Sox (PBA). Retired in 2009.
- The number worn by NCAA basketball legend Bill Spivey. Retired by the University of Kentucky.
- The number of the car Valtteri Bottas drives in F1.
In other fields
Seventy-seven is also:
- 10-77 – the New York City Fire Department's (FDNY) 10 code for high-rise, multiple-dwelling fire 
- Shortening of a 1950's-60's TV series, 77 Sunset Strip
- Group of 77, a group of developing nations at the United Nations
- 77 – Talking Heads's debut album (Talking Heads: 77) released in 1977
- The 77's, an American Rock band
- The On-Line Encyclopedia of Integer Sequences
- Erich Friedman, Stetson University
- The Science behind Sudoku, J.P. Delahaye
- Mersenne Primes: History, Theorems and Lists
- Buchan, Jamie (2010), Easy as Pi: The Countless Ways We Use Numbers Every Day, Penguin, ISBN 9781606522783.
- A Verdict of Mufti Muhammad Hassan
- Imam al-Tahanawi on the Seventy-Seven Branches
- The genealogy of Jesus
- Best Athletes by the numbers
- NC State Football Legend Dennis Byrd Dies at Age of 63