782,740

2² × 5 × 7 × 5591

Starting at 782,740, the Collatz iteration reaches 1 after 131 steps. The first transition is 391370; the starting value is even with 24 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 5 × 7 × 5591

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 1,878,912

Proper Divisor Sum 1,096,172

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #782723 ← → #782777

Radix Representation

Decimal	782740
Binary	10111111000110010100 (20 bits)
Octal	0o2770624
Hexadecimal	0xBF194

Divisor Catalog (24)

1 2 4 5 7 10 14 20 28 35 70 140 5,591 11,182 22,364 27,955 39,137 55,910 78,274 111,820 156,548 195,685 391,370 782,740

Collatz Trajectory (131 steps to reach 1)

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

782,740 391,370 195,685 587,056 293,528 146,764 73,382 36,691 110,074 55,037 165,112 82,556 41,278 20,639 61,918 30,959 92,878 46,439 139,318 69,659 208,978 104,489 313,468 156,734 78,367 235,102 117,551 352,654 176,327 528,982 264,491 793,474 396,737 1,190,212 595,106 297,553 892,660 446,330 223,165 669,496 334,748 167,374 83,687 251,062 125,531 376,594 188,297 564,892 282,446 141,223 423,670 211,835 635,506 317,753 953,260 476,630 238,315 714,946 357,473 1,072,420

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