77,732

2² × 19433

Starting at 77,732, the Collatz iteration reaches 1 after 107 steps. The first transition is 38866; the starting value is even with 6 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 19433

Distinct Prime Factors 2

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 6

Divisor Sum (σ) 136,038

Proper Divisor Sum 58,306

Digit Sum / Digital Root 26 (Root: 8)

Adjacent Primes #77731 ← → #77743

Radix Representation

Decimal	77732
Binary	10010111110100100 (17 bits)
Octal	0o227644
Hexadecimal	0x12FA4

Divisor Catalog (6)

1 2 4 19,433 38,866 77,732

Collatz Trajectory (107 steps to reach 1)

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

77,732 38,866 19,433 58,300 29,150 14,575 43,726 21,863 65,590 32,795 98,386 49,193 147,580 73,790 36,895 110,686 55,343 166,030 83,015 249,046 124,523 373,570 186,785 560,356 280,178 140,089 420,268 210,134 105,067 315,202 157,601 472,804 236,402 118,201 354,604 177,302 88,651 265,954 132,977 398,932 199,466 99,733 299,200 149,600 74,800 37,400 18,700 9,350 4,675 14,026 7,013 21,040 10,520 5,260 2,630 1,315 3,946 1,973 5,920 2,960

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