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Atlas › Integer Profiles › Node 8,002,572

8,002,572

22 × 3 × 19 × 35099
Abundant Even Composite

8,002,572 factors as 2^2 × 3 × 19 × 35099. Its 24 positive divisors give a proper-divisor sum of 11,653,428, so this integer is abundant. The Collatz stopping time is 93 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 19 × 35099
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 19,656,000
Proper Divisor Sum 11,653,428
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #8002559 ← → #8002573

Radix Representation

Decimal 8002572
Binary 11110100001110000001100 (23 bits)
Octal 0o36416014
Hexadecimal 0x7A1C0C

Divisor Catalog (24)

1 2 3 4 6 12 19 38 57 76 114 228 35,099 70,198 105,297 140,396 210,594 421,188 666,881 1,333,762 2,000,643 2,667,524 4,001,286 8,002,572

Collatz Trajectory (93 steps to reach 1)

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

8,002,572 4,001,286 2,000,643 6,001,930 3,000,965 9,002,896 4,501,448 2,250,724 1,125,362 562,681 1,688,044 844,022 422,011 1,266,034 633,017 1,899,052 949,526 474,763 1,424,290 712,145 2,136,436 1,068,218 534,109 1,602,328 801,164 400,582 200,291 600,874 300,437 901,312 450,656 225,328 112,664 56,332 28,166 14,083 42,250 21,125 63,376 31,688 15,844 7,922 3,961 11,884 5,942 2,971 8,914 4,457 13,372 6,686 3,343 10,030 5,015 15,046 7,523 22,570 11,285 33,856 16,928 8,464

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