7,653,632

2⁸ × 7 × 4271

Starting at 7,653,632, the Collatz iteration reaches 1 after 80 steps. The first transition is 3826816; the starting value is even with 36 positive divisors.

Prime Factor Structure

Factorization String 2^8 × 7 × 4271

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 17,463,936

Proper Divisor Sum 9,810,304

Digit Sum / Digital Root 32 (Root: 5)

Adjacent Primes #7653631 ← → #7653649

Radix Representation

Decimal	7653632
Binary	11101001100100100000000 (23 bits)
Octal	0o35144400
Hexadecimal	0x74C900

Divisor Catalog (36)

1 2 4 7 8 14 16 28 32 56 64 112 128 224 256 448 896 1,792 4,271 8,542 17,084 29,897 34,168 59,794 68,336 119,588 136,672 239,176 273,344 478,352 546,688 956,704 1,093,376 1,913,408 3,826,816 7,653,632

Collatz Trajectory (80 steps to reach 1)

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

7,653,632 3,826,816 1,913,408 956,704 478,352 239,176 119,588 59,794 29,897 89,692 44,846 22,423 67,270 33,635 100,906 50,453 151,360 75,680 37,840 18,920 9,460 4,730 2,365 7,096 3,548 1,774 887 2,662 1,331 3,994 1,997 5,992 2,996 1,498 749 2,248 1,124 562 281 844 422 211 634 317 952 476 238 119 358 179 538 269 808 404 202 101 304 152 76 38

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