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Atlas › Integer Profiles › Node 7,200,765

7,200,765

33 × 5 × 11 × 13 × 373
Abundant Odd Composite

7,200,765 factors as 3^3 × 5 × 11 × 13 × 373. Its 64 positive divisors give a proper-divisor sum of 7,878,915, so this integer is abundant. The Collatz stopping time is 372 steps.

Prime Factor Structure

Factorization String 3^3 × 5 × 11 × 13 × 373
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 15,079,680
Proper Divisor Sum 7,878,915
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #7200763 ← → #7200769

Radix Representation

Decimal 7200765
Binary 11011011101111111111101 (23 bits)
Octal 0o33357775
Hexadecimal 0x6DDFFD

Divisor Catalog (60 of 64)

1 3 5 9 11 13 15 27 33 39 45 55 65 99 117 135 143 165 195 297 351 373 429 495 585 715 1,119 1,287 1,485 1,755 1,865 2,145 3,357 3,861 4,103 4,849 5,595 6,435 10,071 12,309 14,547 16,785 19,305 20,515 24,245 36,927 43,641 50,355 53,339 61,545 72,735 110,781 130,923 160,017 184,635 218,205 266,695 480,051 553,905 654,615

Collatz Trajectory (372 steps to reach 1)

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

7,200,765 21,602,296 10,801,148 5,400,574 2,700,287 8,100,862 4,050,431 12,151,294 6,075,647 18,226,942 9,113,471 27,340,414 13,670,207 41,010,622 20,505,311 61,515,934 30,757,967 92,273,902 46,136,951 138,410,854 69,205,427 207,616,282 103,808,141 311,424,424 155,712,212 77,856,106 38,928,053 116,784,160 58,392,080 29,196,040 14,598,020 7,299,010 3,649,505 10,948,516 5,474,258 2,737,129 8,211,388 4,105,694 2,052,847 6,158,542 3,079,271 9,237,814 4,618,907 13,856,722 6,928,361 20,785,084 10,392,542 5,196,271 15,588,814 7,794,407 23,383,222 11,691,611 35,074,834 17,537,417 52,612,252 26,306,126 13,153,063 39,459,190 19,729,595 59,188,786

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