36,738

2 × 3² × 13 × 157

Starting at 36,738, the Collatz iteration reaches 1 after 62 steps. The first transition is 18369; the starting value is even with 24 positive divisors.

Prime Factor Structure

Factorization String 2 × 3^2 × 13 × 157

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 86,268

Proper Divisor Sum 49,530

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #36721 ← → #36739

Radix Representation

Decimal	36738
Binary	1000111110000010 (16 bits)
Octal	0o107602
Hexadecimal	0x8F82

Divisor Catalog (24)

1 2 3 6 9 13 18 26 39 78 117 157 234 314 471 942 1,413 2,041 2,826 4,082 6,123 12,246 18,369 36,738

Collatz Trajectory (62 steps to reach 1)

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

36,738 18,369 55,108 27,554 13,777 41,332 20,666 10,333 31,000 15,500 7,750 3,875 11,626 5,813 17,440 8,720 4,360 2,180 1,090 545 1,636 818 409 1,228 614 307 922 461 1,384 692 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8

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