MathQuarryCalculators

Numbers / 888

888 — a lucky repdigit

888 is composite: factorization 2^3 × 3 × 37. That gives 888 exactly 16 divisors: 1, 2, 3, 4, 6, 8, 12, 24, 37, 74, 111, 148, 222, 296, 444, 888. 888's proper divisors total 1392, 504 more than 888 itself, so 888 is abundant. 888 is also a palindrome, since 888 reads identically forwards and backwards. 888 has a digit sum of 24; for 888, the digital root works out to 6. 888: 2, 3, 4, 6, 8, 12 all divide 888 evenly, out of 2-12. 888 is 1101111000 in binary and 378 in hex; as a Roman numeral it's DCCCLXXXVIII.

Factors
1, 2, 3, 4, 6, 8, 12, 24, 37, 74, 111, 148, 222, 296, 444, 888
Number of factors
16
Prime?
No
Prime factorization
2^3 x 3 x 37
Even or odd
Even
Square
788544
Cube
700227072
Binary
1101111000
Hexadecimal
378
Roman numeral
DCCCLXXXVIII
Perfect square?
No
Perfect cube?
No
Perfect number?
No
Triangular number?
No
Fibonacci number?
No

In Chinese culture, 8 is widely considered the luckiest digit, for a reason rooted directly in language rather than mathematics: in Mandarin, "eight" (八, bā) sounds close to "prosper" or "wealth" (发, fā, as in 发财, fācái, "to get rich"). Because that phonetic resemblance holds across several Chinese dialects, not just Mandarin, the association runs deep and wide across Chinese-speaking communities, and repeating the digit — 88, 888, 8888 — is popularly understood to compound the auspicious meaning rather than dilute it.

This isn't a vague folk belief without real-world consequences; it has measurable economic effects. Phone numbers, license plates, and street addresses containing multiple 8s have documented histories of selling at significant premiums in China and other Chinese-speaking regions, sometimes for tens of thousands of dollars for a single especially "lucky" number, a phenomenon extensively covered in business and cultural journalism over the past several decades. The most famous single instance of this cultural weight shaping a real, planned event: the 2008 Beijing Summer Olympics deliberately opened its ceremony on 8/8/2008 at 8:08:08 pm local time — a date and time chosen explicitly, and publicly acknowledged by organizers, for its concentration of 8s, treated as an auspicious alignment for the Games.

Mathematically, 888 is a repdigit (three repeated 8s), which places it in the same structural family as 111, 222, 333, and every other three-digit repdigit — all divisible by 111 (=3×37), since a repeated-digit number ddd always equals d × 111. For 888: 8 × 111 = 888, and factoring further, 888 = 2³ × 3 × 37. It's also worth noting that 888 is the only three-digit repdigit whose digit is itself a power of 2 greater than 2 (8 = 2³), which gives its full factorization an unusually clean structure: three factors of 2 from the digit itself, plus the 3 × 37 shared by every repdigit in this range.

Beyond the specifically Chinese cultural association, 888 (and 8 more broadly) shows up in numerology traditions elsewhere too, including the Western "angel numbers" belief system, where 888 is commonly interpreted as signaling abundance or financial flow — again worth noting honestly as a documented belief system rather than a provable property, distinct from 888's genuine, checkable status as a repdigit divisible by 3 and 37.

As a plain integer, 888's divisors are 1, 2, 3, 4, 6, 8, 12, 24, 37, 74, 111, 148, 222, 296, 444, and 888 — sixteen divisors total, a direct consequence of its prime factorization (2³ × 3¹ × 37¹) via the standard divisor-counting formula ((3+1)×(1+1)×(1+1)=16). It isn't prime, isn't a perfect square, and doesn't belong to any of the other classic named sequences tracked elsewhere on this site — its fame rests almost entirely on linguistic and cultural association rather than any deeper mathematical structure.

Turned upside down, "888" reads as itself — a genuinely rare property among three-digit repdigits, since 8 is one of only a handful of digits (alongside 0, 1) that looks the same rotated 180 degrees in most common digital and printed typefaces, making 888 visually symmetric under rotation in a way most other numbers simply aren't. This is unrelated to, and considerably more incidental than, its Chinese-language luck association, but it's a small additional reason the digit 8 tends to be perceived as visually clean or "balanced" independent of any cultural meaning attached to it, a purely visual property that has nothing at all to do with its separate, unrelated fame in Chinese-language luck traditions.

The economic premium attached to 8-heavy phone numbers and license plates has been documented in multiple specific, individually reported auction sales — including license plates and phone numbers in Hong Kong, mainland China, and other Chinese-speaking markets fetching prices well into six or seven figures (in US dollar terms) for a single especially favorable number, a genuinely striking real-world dollar value attached directly to a linguistic coincidence rather than to anything about the number's mathematical properties. Regulators and telecom authorities in several of these markets have occasionally had to formally address how "lucky" numbers get allocated, precisely because ordinary lottery-style random assignment can otherwise create real disputes over who receives an especially valuable digit combination, with some jurisdictions eventually moving to formal public auctions specifically to handle allocation of the most sought-after digit sequences transparently.