7,645,216

2⁵ × 173 × 1381

Starting at 7,645,216, the Collatz iteration reaches 1 after 80 steps. The first transition is 3822608; the starting value is even with 24 positive divisors.

Prime Factor Structure

Factorization String 2^5 × 173 × 1381

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 15,149,484

Proper Divisor Sum 7,504,268

Digit Sum / Digital Root 31 (Root: 4)

Adjacent Primes #7645171 ← → #7645219

Radix Representation

Decimal	7645216
Binary	11101001010100000100000 (23 bits)
Octal	0o35124040
Hexadecimal	0x74A820

Divisor Catalog (24)

1 2 4 8 16 32 173 346 692 1,381 1,384 2,762 2,768 5,524 5,536 11,048 22,096 44,192 238,913 477,826 955,652 1,911,304 3,822,608 7,645,216

Collatz Trajectory (80 steps to reach 1)

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

7,645,216 3,822,608 1,911,304 955,652 477,826 238,913 716,740 358,370 179,185 537,556 268,778 134,389 403,168 201,584 100,792 50,396 25,198 12,599 37,798 18,899 56,698 28,349 85,048 42,524 21,262 10,631 31,894 15,947 47,842 23,921 71,764 35,882 17,941 53,824 26,912 13,456 6,728 3,364 1,682 841 2,524 1,262 631 1,894 947 2,842 1,421 4,264 2,132 1,066 533 1,600 800 400 200 100 50 25 76 38

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