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Atlas › Integer Profiles › Node 8,461,024

8,461,024

25 × 11 × 13 × 432
Abundant Even Composite

8,461,024 factors as 2^5 × 11 × 13 × 43^2. Its 72 positive divisors give a proper-divisor sum of 11,574,488, so this integer is abundant. The Collatz stopping time is 305 steps.

Prime Factor Structure

Factorization String 2^5 × 11 × 13 × 43^2
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 20,035,512
Proper Divisor Sum 11,574,488
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #8461021 ← → #8461039

Radix Representation

Decimal 8461024
Binary 100000010001101011100000 (24 bits)
Octal 0o40215340
Hexadecimal 0x811AE0

Divisor Catalog (60 of 72)

1 2 4 8 11 13 16 22 26 32 43 44 52 86 88 104 143 172 176 208 286 344 352 416 473 559 572 688 946 1,118 1,144 1,376 1,849 1,892 2,236 2,288 3,698 3,784 4,472 4,576 6,149 7,396 7,568 8,944 12,298 14,792 15,136 17,888 20,339 24,037 24,596 29,584 40,678 48,074 49,192 59,168 81,356 96,148 98,384 162,712

Collatz Trajectory (305 steps to reach 1)

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

8,461,024 4,230,512 2,115,256 1,057,628 528,814 264,407 793,222 396,611 1,189,834 594,917 1,784,752 892,376 446,188 223,094 111,547 334,642 167,321 501,964 250,982 125,491 376,474 188,237 564,712 282,356 141,178 70,589 211,768 105,884 52,942 26,471 79,414 39,707 119,122 59,561 178,684 89,342 44,671 134,014 67,007 201,022 100,511 301,534 150,767 452,302 226,151 678,454 339,227 1,017,682 508,841 1,526,524 763,262 381,631 1,144,894 572,447 1,717,342 858,671 2,576,014 1,288,007 3,864,022 1,932,011

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