λ
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Atlas › Integer Profiles › Node 9,677,920

9,677,920

25 × 5 × 7 × 8641
Abundant Even Composite

9,677,920 factors as 2^5 × 5 × 7 × 8641. Its 48 positive divisors give a proper-divisor sum of 16,455,488, so this integer is abundant. The Collatz stopping time is 70 steps.

Prime Factor Structure

Factorization String 2^5 × 5 × 7 × 8641
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 26,133,408
Proper Divisor Sum 16,455,488
Digit Sum / Digital Root 40 (Root: 4)
Adjacent Primes #9677893 ← → #9677923

Radix Representation

Decimal 9677920
Binary 100100111010110001100000 (24 bits)
Octal 0o44726140
Hexadecimal 0x93AC60

Divisor Catalog (48)

1 2 4 5 7 8 10 14 16 20 28 32 35 40 56 70 80 112 140 160 224 280 560 1,120 8,641 17,282 34,564 43,205 60,487 69,128 86,410 120,974 138,256 172,820 241,948 276,512 302,435 345,640 483,896 604,870 691,280 967,792 1,209,740 1,382,560 1,935,584 2,419,480 4,838,960 9,677,920

Collatz Trajectory (70 steps to reach 1)

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

9,677,920 4,838,960 2,419,480 1,209,740 604,870 302,435 907,306 453,653 1,360,960 680,480 340,240 170,120 85,060 42,530 21,265 63,796 31,898 15,949 47,848 23,924 11,962 5,981 17,944 8,972 4,486 2,243 6,730 3,365 10,096 5,048 2,524 1,262 631 1,894 947 2,842 1,421 4,264 2,132 1,066 533 1,600 800 400 200 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52

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