835,520

2⁶ × 5 × 7 × 373

Starting at 835,520, the Collatz iteration reaches 1 after 113 steps. The first transition is 417760; the starting value is even with 56 positive divisors.

Prime Factor Structure

Factorization String 2^6 × 5 × 7 × 373

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 56

Divisor Sum (σ) 2,279,904

Proper Divisor Sum 1,444,384

Digit Sum / Digital Root 23 (Root: 5)

Adjacent Primes #835511 ← → #835531

Radix Representation

Decimal	835520
Binary	11001011111111000000 (20 bits)
Octal	0o3137700
Hexadecimal	0xCBFC0

Divisor Catalog (56)

1 2 4 5 7 8 10 14 16 20 28 32 35 40 56 64 70 80 112 140 160 224 280 320 373 448 560 746 1,120 1,492 1,865 2,240 2,611 2,984 3,730 5,222 5,968 7,460 10,444 11,936 13,055 14,920 20,888 23,872 26,110 29,840 41,776 52,220 59,680 83,552 104,440 119,360 167,104 208,880 417,760 835,520

Collatz Trajectory (113 steps to reach 1)

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

835,520 417,760 208,880 104,440 52,220 26,110 13,055 39,166 19,583 58,750 29,375 88,126 44,063 132,190 66,095 198,286 99,143 297,430 148,715 446,146 223,073 669,220 334,610 167,305 501,916 250,958 125,479 376,438 188,219 564,658 282,329 846,988 423,494 211,747 635,242 317,621 952,864 476,432 238,216 119,108 59,554 29,777 89,332 44,666 22,333 67,000 33,500 16,750 8,375 25,126 12,563 37,690 18,845 56,536 28,268 14,134 7,067 21,202 10,601 31,804

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