7,628,544

2⁸ × 3² × 7 × 11 × 43

7,628,544 factors as 2^8 × 3^2 × 7 × 11 × 43. Its 216 positive divisors give a proper-divisor sum of 20,431,488, so this integer is abundant. The Collatz stopping time is 80 steps.

Prime Factor Structure

Factorization String 2^8 × 3^2 × 7 × 11 × 43

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 216

Divisor Sum (σ) 28,060,032

Proper Divisor Sum 20,431,488

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7628527 ← → #7628561

Radix Representation

Decimal	7628544
Binary	11101000110011100000000 (23 bits)
Octal	0o35063400
Hexadecimal	0x746700

Divisor Catalog (60 of 216)

1 2 3 4 6 7 8 9 11 12 14 16 18 21 22 24 28 32 33 36 42 43 44 48 56 63 64 66 72 77 84 86 88 96 99 112 126 128 129 132 144 154 168 172 176 192 198 224 231 252 256 258 264 288 301 308 336 344 352 384

Collatz Trajectory (80 steps to reach 1)

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

7,628,544 3,814,272 1,907,136 953,568 476,784 238,392 119,196 59,598 29,799 89,398 44,699 134,098 67,049 201,148 100,574 50,287 150,862 75,431 226,294 113,147 339,442 169,721 509,164 254,582 127,291 381,874 190,937 572,812 286,406 143,203 429,610 214,805 644,416 322,208 161,104 80,552 40,276 20,138 10,069 30,208 15,104 7,552 3,776 1,888 944 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38

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