# 77 (number)

 ← 76 77 78 →
Cardinal seventy-seven
Ordinal 77th
(seventy-seventh)
Factorization 7 × 11
Divisors 1, 7, 11, 77
Roman numeral LXXVII
Binary 10011012
Ternary 22123
Quaternary 10314
Quinary 3025
Senary 2056
Octal 1158
Duodecimal 6512
Vigesimal 3H20
Base 36 2536

77 (seventy-seven) is the natural number following 76 and preceding 78. Seventy-seven is the smallest positive integer requiring five syllables in English.

## In mathematics

Seventy-seven is the 22nd discrete biprime and the first of the (7.q) family. Since both 7 and 11 are Gaussian primes, this means that 77 is a Blum integer.

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 also is the number of integer partitions of the number 12.[1]

It is the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1.[2]

77 and 78 form a Ruth–Aaron pair.

It is possible for a sudoku puzzle to have as many as 77 givens, yet lack a unique solution.[3]

It and its sibling 49 are the only 2-digit numbers whose home primes (in base 10) have not been calculated.

It is the number of digits of the 12th perfect number.[4]

## In history

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.[5]

## In religion

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.[6] Some have gone so far as to delineate these branches.[7]

The Gospel of Luke lists 77 generations from Adam to Jesus.[8]

### 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.

## In other fields

Seventy-seven is also: