40,075

5² × 7 × 229

Starting at 40,075, the Collatz iteration reaches 1 after 67 steps. The first transition is 120226; the starting value is odd with 12 positive divisors.

Prime Factor Structure

Factorization String 5^2 × 7 × 229

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 57,040

Proper Divisor Sum 16,965

Digit Sum / Digital Root 16 (Root: 7)

Adjacent Primes #40063 ← → #40087

Radix Representation

Decimal	40075
Binary	1001110010001011 (16 bits)
Octal	0o116213
Hexadecimal	0x9C8B

Divisor Catalog (12)

1 5 7 25 35 175 229 1,145 1,603 5,725 8,015 40,075

Collatz Trajectory (67 steps to reach 1)

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

40,075 120,226 60,113 180,340 90,170 45,085 135,256 67,628 33,814 16,907 50,722 25,361 76,084 38,042 19,021 57,064 28,532 14,266 7,133 21,400 10,700 5,350 2,675 8,026 4,013 12,040 6,020 3,010 1,505 4,516 2,258 1,129 3,388 1,694 847 2,542 1,271 3,814 1,907 5,722 2,861 8,584 4,292 2,146 1,073 3,220 1,610 805 2,416 1,208 604 302 151 454 227 682 341 1,024 512 256

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