How many highly divisible numbers are there from 0 to 1,000,000?

Exactly 2,809 of the 1,000,001 supported numbers match this pattern, which is 1 in 356. The count comes from evaluating every number in the range, not from a sample.

How does this pattern affect a number's rarity score on RNGdle.net?

The pattern contributes -log2(2,809 / 1,000,001) bits of information to the score, in the number theory group. Rarer patterns contribute more, and overlapping patterns within a group are de-duplicated so nothing is counted twice.

Patterns /Number Theory

Highly Divisible Numbers

These numbers have at least a hundred distinct divisors — the opposite extreme from primes, which have exactly two.

Matches in range

2,809

Share of all numbers

1 in 356

Out of

1,000,001

How long might highly divisible numbers take?

1 in 356 per roll · 356 rolls on average.

At one daily specimen a day, the mean is about 1 years. A 50% chance takes 247 rolls; 90% takes 819.

7 daily rolls

1.95%

30 daily rolls

8.09%

365 daily rolls

64.18%

Or choose a number of future rolls

8.09% chance of at least one match in 30 independent rolls.

Waiting times are averages, not deadlines. Previous misses do not increase the next roll’s chance. Only Daily Specimens stamp your Atlas.

Find numbers with this pattern →

Divisor counts come from the exponents in a number's prime factorisation, so reaching a hundred requires several small primes raised to several powers at once. Numbers like 720720 = 2⁴ × 3² × 5 × 7 × 11 × 13 are the result.

This is a demanding threshold: the count above shows how few numbers in the range clear it. Most numbers under a million have fewer than thirty divisors.

Highly divisible numbers are why calendars, clocks and old measurement systems favour 12, 60 and 360 — dividing evenly in many ways is genuinely useful, and genuinely uncommon.

Highest-scoring examples

The best-scoring numbers of four digits or more that carry this pattern. Shorter numbers are excluded here because their length alone dominates any score ranking.

828,828 Top <0.01% Singular 888,888 Top <0.01% Singular 696,696 Top <0.01% Singular 252,252 Top <0.01% Singular 969,696 Top 0.01% Singular 300,300 Top 0.01% Singular 400,400 Top 0.02% Singular 404,040 Top 0.02% Singular

Smallest examples

The first numbers in the range that match this pattern.

45,360 50,400 55,440 60,480 65,520 69,300 70,560 71,280

Related number theory patterns

Prime Numbers

A prime has no divisors other than 1 and itself. They are the building blocks every other number is assembled from.

Semiprime Numbers

A semiprime is a product of exactly two primes, counted with multiplicity — 15 = 3 × 5, and 49 = 7 × 7 counts too.

Perfect Squares

A perfect square is some whole number times itself: 144 = 12², 10000 = 100². The range ends neatly on 1,000,000 = 1000².

Perfect Cubes

A perfect cube is a whole number raised to the third power: 216 = 6³, 970299 = 99³. There are only about a hundred in the entire range.

Powers of Two

Each power of two is double the last: 1, 2, 4, 8, 16, and on up through 1024, 65536 and 524288. Doubling exhausts the range in only twenty steps.

Explore this pattern Analyze a number All patterns