9,880,320

2⁸ × 3 × 5 × 31 × 83

9,880,320 factors as 2^8 × 3 × 5 × 31 × 83. Its 144 positive divisors give a proper-divisor sum of 23,085,312, so this integer is abundant. The Collatz stopping time is 220 steps.

Prime Factor Structure

Factorization String 2^8 × 3 × 5 × 31 × 83

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 144

Divisor Sum (σ) 32,965,632

Proper Divisor Sum 23,085,312

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #9880307 ← → #9880327

Radix Representation

Decimal	9880320
Binary	100101101100001100000000 (24 bits)
Octal	0o45541400
Hexadecimal	0x96C300

Divisor Catalog (60 of 144)

1 2 3 4 5 6 8 10 12 15 16 20 24 30 31 32 40 48 60 62 64 80 83 93 96 120 124 128 155 160 166 186 192 240 248 249 256 310 320 332 372 384 415 465 480 496 498 620 640 664 744 768 830 930 960 992 996 1,240 1,245 1,280

Collatz Trajectory (220 steps to reach 1)

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

9,880,320 4,940,160 2,470,080 1,235,040 617,520 308,760 154,380 77,190 38,595 115,786 57,893 173,680 86,840 43,420 21,710 10,855 32,566 16,283 48,850 24,425 73,276 36,638 18,319 54,958 27,479 82,438 41,219 123,658 61,829 185,488 92,744 46,372 23,186 11,593 34,780 17,390 8,695 26,086 13,043 39,130 19,565 58,696 29,348 14,674 7,337 22,012 11,006 5,503 16,510 8,255 24,766 12,383 37,150 18,575 55,726 27,863 83,590 41,795 125,386 62,693

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