λ
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Atlas › Integer Profiles › Node 8,736,728

8,736,728

23 × 7 × 11 × 13 × 1091
Abundant Even Composite

8,736,728 factors as 2^3 × 7 × 11 × 13 × 1091. Its 64 positive divisors give a proper-divisor sum of 13,277,992, so this integer is abundant. The Collatz stopping time is 88 steps.

Prime Factor Structure

Factorization String 2^3 × 7 × 11 × 13 × 1091
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 22,014,720
Proper Divisor Sum 13,277,992
Digit Sum / Digital Root 41 (Root: 5)
Adjacent Primes #8736727 ← → #8736781

Radix Representation

Decimal 8736728
Binary 100001010100111111011000 (24 bits)
Octal 0o41247730
Hexadecimal 0x854FD8

Divisor Catalog (60 of 64)

1 2 4 7 8 11 13 14 22 26 28 44 52 56 77 88 91 104 143 154 182 286 308 364 572 616 728 1,001 1,091 1,144 2,002 2,182 4,004 4,364 7,637 8,008 8,728 12,001 14,183 15,274 24,002 28,366 30,548 48,004 56,732 61,096 84,007 96,008 99,281 113,464 156,013 168,014 198,562 312,026 336,028 397,124 624,052 672,056 794,248 1,092,091

Collatz Trajectory (88 steps to reach 1)

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

8,736,728 4,368,364 2,184,182 1,092,091 3,276,274 1,638,137 4,914,412 2,457,206 1,228,603 3,685,810 1,842,905 5,528,716 2,764,358 1,382,179 4,146,538 2,073,269 6,219,808 3,109,904 1,554,952 777,476 388,738 194,369 583,108 291,554 145,777 437,332 218,666 109,333 328,000 164,000 82,000 41,000 20,500 10,250 5,125 15,376 7,688 3,844 1,922 961 2,884 1,442 721 2,164 1,082 541 1,624 812 406 203 610 305 916 458 229 688 344 172 86 43

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