827,850

2 × 3 × 5² × 5519

Starting at 827,850, the Collatz iteration reaches 1 after 144 steps. The first transition is 413925; the starting value is even with 24 positive divisors.

Prime Factor Structure

Factorization String 2 × 3 × 5^2 × 5519

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 2,053,440

Proper Divisor Sum 1,225,590

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #827843 ← → #827851

Radix Representation

Decimal	827850
Binary	11001010000111001010 (20 bits)
Octal	0o3120712
Hexadecimal	0xCA1CA

Divisor Catalog (24)

1 2 3 5 6 10 15 25 30 50 75 150 5,519 11,038 16,557 27,595 33,114 55,190 82,785 137,975 165,570 275,950 413,925 827,850

Collatz Trajectory (144 steps to reach 1)

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

827,850 413,925 1,241,776 620,888 310,444 155,222 77,611 232,834 116,417 349,252 174,626 87,313 261,940 130,970 65,485 196,456 98,228 49,114 24,557 73,672 36,836 18,418 9,209 27,628 13,814 6,907 20,722 10,361 31,084 15,542 7,771 23,314 11,657 34,972 17,486 8,743 26,230 13,115 39,346 19,673 59,020 29,510 14,755 44,266 22,133 66,400 33,200 16,600 8,300 4,150 2,075 6,226 3,113 9,340 4,670 2,335 7,006 3,503 10,510 5,255

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