67,520

2⁶ × 5 × 211

Starting at 67,520, the Collatz iteration reaches 1 after 174 steps. The first transition is 33760; the starting value is even with 28 positive divisors.

Prime Factor Structure

Factorization String 2^6 × 5 × 211

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 28

Divisor Sum (σ) 161,544

Proper Divisor Sum 94,024

Digit Sum / Digital Root 20 (Root: 2)

Adjacent Primes #67511 ← → #67523

Radix Representation

Decimal	67520
Binary	10000011111000000 (17 bits)
Octal	0o203700
Hexadecimal	0x107C0

Divisor Catalog (28)

1 2 4 5 8 10 16 20 32 40 64 80 160 211 320 422 844 1,055 1,688 2,110 3,376 4,220 6,752 8,440 13,504 16,880 33,760 67,520

Collatz Trajectory (174 steps to reach 1)

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

67,520 33,760 16,880 8,440 4,220 2,110 1,055 3,166 1,583 4,750 2,375 7,126 3,563 10,690 5,345 16,036 8,018 4,009 12,028 6,014 3,007 9,022 4,511 13,534 6,767 20,302 10,151 30,454 15,227 45,682 22,841 68,524 34,262 17,131 51,394 25,697 77,092 38,546 19,273 57,820 28,910 14,455 43,366 21,683 65,050 32,525 97,576 48,788 24,394 12,197 36,592 18,296 9,148 4,574 2,287 6,862 3,431 10,294 5,147 15,442

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