720,727

7 × 19 × 5419

Starting at 720,727, the Collatz iteration reaches 1 after 66 steps. The first transition is 2162182; the starting value is odd with 8 positive divisors.

Prime Factor Structure

Factorization String 7 × 19 × 5419

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 867,200

Proper Divisor Sum 146,473

Digit Sum / Digital Root 25 (Root: 7)

Adjacent Primes #720703 ← → #720743

Radix Representation

Decimal	720727
Binary	10101111111101010111 (20 bits)
Octal	0o2577527
Hexadecimal	0xAFF57

Divisor Catalog (8)

1 7 19 133 5,419 37,933 102,961 720,727

Collatz Trajectory (66 steps to reach 1)

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

720,727 2,162,182 1,081,091 3,243,274 1,621,637 4,864,912 2,432,456 1,216,228 608,114 304,057 912,172 456,086 228,043 684,130 342,065 1,026,196 513,098 256,549 769,648 384,824 192,412 96,206 48,103 144,310 72,155 216,466 108,233 324,700 162,350 81,175 243,526 121,763 365,290 182,645 547,936 273,968 136,984 68,492 34,246 17,123 51,370 25,685 77,056 38,528 19,264 9,632 4,816 2,408 1,204 602 301 904 452 226 113 340 170 85 256 128

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