47,460

2² × 3 × 5 × 7 × 113

Starting at 47,460, the Collatz iteration reaches 1 after 75 steps. The first transition is 23730; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3 × 5 × 7 × 113

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 153,216

Proper Divisor Sum 105,756

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #47459 ← → #47491

Radix Representation

Decimal	47460
Binary	1011100101100100 (16 bits)
Octal	0o134544
Hexadecimal	0xB964

Divisor Catalog (48)

1 2 3 4 5 6 7 10 12 14 15 20 21 28 30 35 42 60 70 84 105 113 140 210 226 339 420 452 565 678 791 1,130 1,356 1,582 1,695 2,260 2,373 3,164 3,390 3,955 4,746 6,780 7,910 9,492 11,865 15,820 23,730 47,460

Collatz Trajectory (75 steps to reach 1)

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

47,460 23,730 11,865 35,596 17,798 8,899 26,698 13,349 40,048 20,024 10,012 5,006 2,503 7,510 3,755 11,266 5,633 16,900 8,450 4,225 12,676 6,338 3,169 9,508 4,754 2,377 7,132 3,566 1,783 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

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