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Atlas › Integer Profiles › Node 9,706,840

9,706,840

23 × 5 × 11 × 13 × 1697
Abundant Even Composite

9,706,840 factors as 2^3 × 5 × 11 × 13 × 1697. Its 64 positive divisors give a proper-divisor sum of 15,966,920, so this integer is abundant. The Collatz stopping time is 238 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 11 × 13 × 1697
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 25,673,760
Proper Divisor Sum 15,966,920
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #9706831 ← → #9706841

Radix Representation

Decimal 9706840
Binary 100101000001110101011000 (24 bits)
Octal 0o45016530
Hexadecimal 0x941D58

Divisor Catalog (60 of 64)

1 2 4 5 8 10 11 13 20 22 26 40 44 52 55 65 88 104 110 130 143 220 260 286 440 520 572 715 1,144 1,430 1,697 2,860 3,394 5,720 6,788 8,485 13,576 16,970 18,667 22,061 33,940 37,334 44,122 67,880 74,668 88,244 93,335 110,305 149,336 176,488 186,670 220,610 242,671 373,340 441,220 485,342 746,680 882,440 970,684 1,213,355

Collatz Trajectory (238 steps to reach 1)

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

9,706,840 4,853,420 2,426,710 1,213,355 3,640,066 1,820,033 5,460,100 2,730,050 1,365,025 4,095,076 2,047,538 1,023,769 3,071,308 1,535,654 767,827 2,303,482 1,151,741 3,455,224 1,727,612 863,806 431,903 1,295,710 647,855 1,943,566 971,783 2,915,350 1,457,675 4,373,026 2,186,513 6,559,540 3,279,770 1,639,885 4,919,656 2,459,828 1,229,914 614,957 1,844,872 922,436 461,218 230,609 691,828 345,914 172,957 518,872 259,436 129,718 64,859 194,578 97,289 291,868 145,934 72,967 218,902 109,451 328,354 164,177 492,532 246,266 123,133 369,400

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