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Atlas › Integer Profiles › Node 8,315,664

8,315,664

24 × 3 × 7 × 24749
Abundant Even Composite

8,315,664 factors as 2^4 × 3 × 7 × 24749. Its 40 positive divisors give a proper-divisor sum of 16,236,336, so this integer is abundant. The Collatz stopping time is 137 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 7 × 24749
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 24,552,000
Proper Divisor Sum 16,236,336
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #8315651 ← → #8315689

Radix Representation

Decimal 8315664
Binary 11111101110001100010000 (23 bits)
Octal 0o37561420
Hexadecimal 0x7EE310

Divisor Catalog (40)

1 2 3 4 6 7 8 12 14 16 21 24 28 42 48 56 84 112 168 336 24,749 49,498 74,247 98,996 148,494 173,243 197,992 296,988 346,486 395,984 519,729 593,976 692,972 1,039,458 1,187,952 1,385,944 2,078,916 2,771,888 4,157,832 8,315,664

Collatz Trajectory (137 steps to reach 1)

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

8,315,664 4,157,832 2,078,916 1,039,458 519,729 1,559,188 779,594 389,797 1,169,392 584,696 292,348 146,174 73,087 219,262 109,631 328,894 164,447 493,342 246,671 740,014 370,007 1,110,022 555,011 1,665,034 832,517 2,497,552 1,248,776 624,388 312,194 156,097 468,292 234,146 117,073 351,220 175,610 87,805 263,416 131,708 65,854 32,927 98,782 49,391 148,174 74,087 222,262 111,131 333,394 166,697 500,092 250,046 125,023 375,070 187,535 562,606 281,303 843,910 421,955 1,265,866 632,933 1,898,800

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