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Atlas › Integer Profiles › Node 8,672,000

8,672,000

28 × 53 × 271
Abundant Even Composite

8,672,000 factors as 2^8 × 5^3 × 271. Its 72 positive divisors give a proper-divisor sum of 13,010,752, so this integer is abundant. The Collatz stopping time is 155 steps.

Prime Factor Structure

Factorization String 2^8 × 5^3 × 271
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 21,682,752
Proper Divisor Sum 13,010,752
Digit Sum / Digital Root 23 (Root: 5)
Adjacent Primes #8671991 ← → #8672003

Radix Representation

Decimal 8672000
Binary 100001000101001100000000 (24 bits)
Octal 0o41051400
Hexadecimal 0x845300

Divisor Catalog (60 of 72)

1 2 4 5 8 10 16 20 25 32 40 50 64 80 100 125 128 160 200 250 256 271 320 400 500 542 640 800 1,000 1,084 1,280 1,355 1,600 2,000 2,168 2,710 3,200 4,000 4,336 5,420 6,400 6,775 8,000 8,672 10,840 13,550 16,000 17,344 21,680 27,100 32,000 33,875 34,688 43,360 54,200 67,750 69,376 86,720 108,400 135,500

Collatz Trajectory (155 steps to reach 1)

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

8,672,000 4,336,000 2,168,000 1,084,000 542,000 271,000 135,500 67,750 33,875 101,626 50,813 152,440 76,220 38,110 19,055 57,166 28,583 85,750 42,875 128,626 64,313 192,940 96,470 48,235 144,706 72,353 217,060 108,530 54,265 162,796 81,398 40,699 122,098 61,049 183,148 91,574 45,787 137,362 68,681 206,044 103,022 51,511 154,534 77,267 231,802 115,901 347,704 173,852 86,926 43,463 130,390 65,195 195,586 97,793 293,380 146,690 73,345 220,036 110,018 55,009

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