8,221,473

3³ × 13 × 59 × 397

8,221,473 has the prime decomposition 3^3 × 13 × 59 × 397. Its 4 distinct prime factors produce 32 positive divisors.

Prime Factor Structure

Factorization String 3^3 × 13 × 59 × 397

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 13,372,800

Proper Divisor Sum 5,151,327

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #8221469 ← → #8221487

Radix Representation

Decimal	8221473
Binary	11111010111001100100001 (23 bits)
Octal	0o37271441
Hexadecimal	0x7D7321

Divisor Catalog (32)

1 3 9 13 27 39 59 117 177 351 397 531 767 1,191 1,593 2,301 3,573 5,161 6,903 10,719 15,483 20,709 23,423 46,449 70,269 139,347 210,807 304,499 632,421 913,497 2,740,491 8,221,473

Collatz Trajectory (111 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

8,221,473 24,664,420 12,332,210 6,166,105 18,498,316 9,249,158 4,624,579 13,873,738 6,936,869 20,810,608 10,405,304 5,202,652 2,601,326 1,300,663 3,901,990 1,950,995 5,852,986 2,926,493 8,779,480 4,389,740 2,194,870 1,097,435 3,292,306 1,646,153 4,938,460 2,469,230 1,234,615 3,703,846 1,851,923 5,555,770 2,777,885 8,333,656 4,166,828 2,083,414 1,041,707 3,125,122 1,562,561 4,687,684 2,343,842 1,171,921 3,515,764 1,757,882 878,941 2,636,824 1,318,412 659,206 329,603 988,810 494,405 1,483,216 741,608 370,804 185,402 92,701 278,104 139,052 69,526 34,763 104,290 52,145

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