45,225

3³ × 5² × 67

45,225 is odd and not a perfect square. Its factorization is 3^3 × 5^2 × 67 and its 24 divisors sum to 84,320.

Prime Factor Structure

Factorization String 3^3 × 5^2 × 67

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 84,320

Proper Divisor Sum 39,095

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #45197 ← → #45233

Radix Representation

Decimal	45225
Binary	1011000010101001 (16 bits)
Octal	0o130251
Hexadecimal	0xB0A9

Divisor Catalog (24)

1 3 5 9 15 25 27 45 67 75 135 201 225 335 603 675 1,005 1,675 1,809 3,015 5,025 9,045 15,075 45,225

Collatz Trajectory (62 steps to reach 1)

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

45,225 135,676 67,838 33,919 101,758 50,879 152,638 76,319 228,958 114,479 343,438 171,719 515,158 257,579 772,738 386,369 1,159,108 579,554 289,777 869,332 434,666 217,333 652,000 326,000 163,000 81,500 40,750 20,375 61,126 30,563 91,690 45,845 137,536 68,768 34,384 17,192 8,596 4,298 2,149 6,448 3,224 1,612 806 403 1,210 605 1,816 908 454 227 682 341 1,024 512 256 128 64 32 16 8

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