Number reference
777 explained.
777: seven hundred seventy-seven, composite, repdigit; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- seven hundred seventy-seven
- Classification
- composite
- Factors
- 1, 3, 7, 21, 37, 111, 259, 777
- Prime factorization
- 3 × 7 × 37
- Square root
- 27.87472
- Cube root
- 9.193347
- Binary
- 1100001001
- Octal
- 1411
- Hexadecimal
- 309
- Roman numeral
- DCCLXXVII
- Digit sum
- 21
- Digital root
- 3
What makes 777 notable
- Repdigit. 777 is written with a single repeated digit, so it is divisible by the repunit of the same length.
777 in everyday use
Seven hundred seventy-seven is the jackpot: three sevens is the classic winning line on a slot machine, which is why the number is used to mean luck in casinos and on scratch cards. Boeing chose it for its long-range twin-engine jet, the 777, first flown in 1994 and now among the most widely used wide-body airliners. In Unix and Linux, chmod 777 grants read, write, and execute permission to everyone, a setting that administrators recognise instantly and generally discourage.
That last use works because each 7 is 111 in binary, so 777 in octal is nine ones. In decimal the number factors as 3 × 7 × 37, three distinct primes, which makes it sphenic with eight divisors. Like every three-digit repdigit it is a multiple of 111, and 777 ÷ 37 = 21. It is 1100001001 in binary and 309 in hexadecimal. Its digit sum is 21, which divides it, so it is a Harshad number.
Nearby numbers
How to read this page
The factor list shows every way 777 splits into equal whole-number groups — 8 divisors in total. The prime factorisation is the compact form of that same information, and the base conversions restate 777 for contexts that do not use decimal.
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