780,440

2³ × 5 × 109 × 179

Starting at 780,440, the Collatz iteration reaches 1 after 131 steps. The first transition is 390220; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 5 × 109 × 179

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 1,782,000

Proper Divisor Sum 1,001,560

Digit Sum / Digital Root 23 (Root: 5)

Adjacent Primes #780433 ← → #780457

Radix Representation

Decimal	780440
Binary	10111110100010011000 (20 bits)
Octal	0o2764230
Hexadecimal	0xBE898

Divisor Catalog (32)

1 2 4 5 8 10 20 40 109 179 218 358 436 545 716 872 895 1,090 1,432 1,790 2,180 3,580 4,360 7,160 19,511 39,022 78,044 97,555 156,088 195,110 390,220 780,440

Collatz Trajectory (131 steps to reach 1)

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

780,440 390,220 195,110 97,555 292,666 146,333 439,000 219,500 109,750 54,875 164,626 82,313 246,940 123,470 61,735 185,206 92,603 277,810 138,905 416,716 208,358 104,179 312,538 156,269 468,808 234,404 117,202 58,601 175,804 87,902 43,951 131,854 65,927 197,782 98,891 296,674 148,337 445,012 222,506 111,253 333,760 166,880 83,440 41,720 20,860 10,430 5,215 15,646 7,823 23,470 11,735 35,206 17,603 52,810 26,405 79,216 39,608 19,804 9,902 4,951

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