688,153

83 × 8291

Starting at 688,153, the Collatz iteration reaches 1 after 154 steps. The first transition is 2064460; the starting value is odd with 4 positive divisors.

Prime Factor Structure

Factorization String 83 × 8291

Distinct Prime Factors 2

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 4

Divisor Sum (σ) 696,528

Proper Divisor Sum 8,375

Digit Sum / Digital Root 31 (Root: 4)

Adjacent Primes #688147 ← → #688159

Radix Representation

Decimal	688153
Binary	10101000000000011001 (20 bits)
Octal	0o2500031
Hexadecimal	0xA8019

Divisor Catalog (4)

1 83 8,291 688,153

Collatz Trajectory (154 steps to reach 1)

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

688,153 2,064,460 1,032,230 516,115 1,548,346 774,173 2,322,520 1,161,260 580,630 290,315 870,946 435,473 1,306,420 653,210 326,605 979,816 489,908 244,954 122,477 367,432 183,716 91,858 45,929 137,788 68,894 34,447 103,342 51,671 155,014 77,507 232,522 116,261 348,784 174,392 87,196 43,598 21,799 65,398 32,699 98,098 49,049 147,148 73,574 36,787 110,362 55,181 165,544 82,772 41,386 20,693 62,080 31,040 15,520 7,760 3,880 1,940 970 485 1,456 728

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