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Atlas › Integer Profiles › Node 9,306,072

9,306,072

23 × 32 × 17 × 7603
Abundant Even Composite

9,306,072 factors as 2^3 × 3^2 × 17 × 7603. Its 48 positive divisors give a proper-divisor sum of 17,383,968, so this integer is abundant. The Collatz stopping time is 101 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 17 × 7603
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 26,690,040
Proper Divisor Sum 17,383,968
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #9306049 ← → #9306079

Radix Representation

Decimal 9306072
Binary 100011011111111111011000 (24 bits)
Octal 0o43377730
Hexadecimal 0x8DFFD8

Divisor Catalog (48)

1 2 3 4 6 8 9 12 17 18 24 34 36 51 68 72 102 136 153 204 306 408 612 1,224 7,603 15,206 22,809 30,412 45,618 60,824 68,427 91,236 129,251 136,854 182,472 258,502 273,708 387,753 517,004 547,416 775,506 1,034,008 1,163,259 1,551,012 2,326,518 3,102,024 4,653,036 9,306,072

Collatz Trajectory (101 steps to reach 1)

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

9,306,072 4,653,036 2,326,518 1,163,259 3,489,778 1,744,889 5,234,668 2,617,334 1,308,667 3,926,002 1,963,001 5,889,004 2,944,502 1,472,251 4,416,754 2,208,377 6,625,132 3,312,566 1,656,283 4,968,850 2,484,425 7,453,276 3,726,638 1,863,319 5,589,958 2,794,979 8,384,938 4,192,469 12,577,408 6,288,704 3,144,352 1,572,176 786,088 393,044 196,522 98,261 294,784 147,392 73,696 36,848 18,424 9,212 4,606 2,303 6,910 3,455 10,366 5,183 15,550 7,775 23,326 11,663 34,990 17,495 52,486 26,243 78,730 39,365 118,096 59,048

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