7,726,080

2¹⁰ × 3 × 5 × 503

Starting at 7,726,080, the Collatz iteration reaches 1 after 80 steps. The first transition is 3863040; the starting value is even with 88 positive divisors.

Prime Factor Structure

Factorization String 2^10 × 3 × 5 × 503

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 88

Divisor Sum (σ) 24,760,512

Proper Divisor Sum 17,034,432

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #7726079 ← → #7726087

Radix Representation

Decimal	7726080
Binary	11101011110010000000000 (23 bits)
Octal	0o35362000
Hexadecimal	0x75E400

Divisor Catalog (60 of 88)

1 2 3 4 5 6 8 10 12 15 16 20 24 30 32 40 48 60 64 80 96 120 128 160 192 240 256 320 384 480 503 512 640 768 960 1,006 1,024 1,280 1,509 1,536 1,920 2,012 2,515 2,560 3,018 3,072 3,840 4,024 5,030 5,120 6,036 7,545 7,680 8,048 10,060 12,072 15,090 15,360 16,096 20,120

Collatz Trajectory (80 steps to reach 1)

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

7,726,080 3,863,040 1,931,520 965,760 482,880 241,440 120,720 60,360 30,180 15,090 7,545 22,636 11,318 5,659 16,978 8,489 25,468 12,734 6,367 19,102 9,551 28,654 14,327 42,982 21,491 64,474 32,237 96,712 48,356 24,178 12,089 36,268 18,134 9,067 27,202 13,601 40,804 20,402 10,201 30,604 15,302 7,651 22,954 11,477 34,432 17,216 8,608 4,304 2,152 1,076 538 269 808 404 202 101 304 152 76 38

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