867,825

3² × 5² × 7 × 19 × 29

867,825 has the prime decomposition 3^2 × 5^2 × 7 × 19 × 29. Its 5 distinct prime factors produce 72 positive divisors.

Prime Factor Structure

Factorization String 3^2 × 5^2 × 7 × 19 × 29

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 1,934,400

Proper Divisor Sum 1,066,575

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #867817 ← → #867827

Radix Representation

Decimal	867825
Binary	11010011110111110001 (20 bits)
Octal	0o3236761
Hexadecimal	0xD3DF1

Divisor Catalog (60 of 72)

1 3 5 7 9 15 19 21 25 29 35 45 57 63 75 87 95 105 133 145 171 175 203 225 261 285 315 399 435 475 525 551 609 665 725 855 1,015 1,197 1,305 1,425 1,575 1,653 1,827 1,995 2,175 2,755 3,045 3,325 3,857 4,275 4,959 5,075 5,985 6,525 8,265 9,135 9,975 11,571 13,775 15,225

Collatz Trajectory (188 steps to reach 1)

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

867,825 2,603,476 1,301,738 650,869 1,952,608 976,304 488,152 244,076 122,038 61,019 183,058 91,529 274,588 137,294 68,647 205,942 102,971 308,914 154,457 463,372 231,686 115,843 347,530 173,765 521,296 260,648 130,324 65,162 32,581 97,744 48,872 24,436 12,218 6,109 18,328 9,164 4,582 2,291 6,874 3,437 10,312 5,156 2,578 1,289 3,868 1,934 967 2,902 1,451 4,354 2,177 6,532 3,266 1,633 4,900 2,450 1,225 3,676 1,838 919

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