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Atlas › Integer Profiles › Node 7,207,326

7,207,326

2 × 33 × 7 × 23 × 829
Abundant Even Composite

7,207,326 factors as 2 × 3^3 × 7 × 23 × 829. Its 64 positive divisors give a proper-divisor sum of 11,915,874, so this integer is abundant. The Collatz stopping time is 235 steps.

Prime Factor Structure

Factorization String 2 × 3^3 × 7 × 23 × 829
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 19,123,200
Proper Divisor Sum 11,915,874
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #7207301 ← → #7207331

Radix Representation

Decimal 7207326
Binary 11011011111100110011110 (23 bits)
Octal 0o33374636
Hexadecimal 0x6DF99E

Divisor Catalog (60 of 64)

1 2 3 6 7 9 14 18 21 23 27 42 46 54 63 69 126 138 161 189 207 322 378 414 483 621 829 966 1,242 1,449 1,658 2,487 2,898 4,347 4,974 5,803 7,461 8,694 11,606 14,922 17,409 19,067 22,383 34,818 38,134 44,766 52,227 57,201 104,454 114,402 133,469 156,681 171,603 266,938 313,362 343,206 400,407 514,809 800,814 1,029,618

Collatz Trajectory (235 steps to reach 1)

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

7,207,326 3,603,663 10,810,990 5,405,495 16,216,486 8,108,243 24,324,730 12,162,365 36,487,096 18,243,548 9,121,774 4,560,887 13,682,662 6,841,331 20,523,994 10,261,997 30,785,992 15,392,996 7,696,498 3,848,249 11,544,748 5,772,374 2,886,187 8,658,562 4,329,281 12,987,844 6,493,922 3,246,961 9,740,884 4,870,442 2,435,221 7,305,664 3,652,832 1,826,416 913,208 456,604 228,302 114,151 342,454 171,227 513,682 256,841 770,524 385,262 192,631 577,894 288,947 866,842 433,421 1,300,264 650,132 325,066 162,533 487,600 243,800 121,900 60,950 30,475 91,426 45,713

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