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Atlas › Integer Profiles › Node 68,309,040

68,309,040

24 × 3 × 5 × 241 × 1181
Abundant Even Composite

68,309,040 factors as 2^4 × 3 × 5 × 241 × 1181. Its 80 positive divisors give a proper-divisor sum of 144,507,696, so this integer is abundant. The Collatz stopping time is 215 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 5 × 241 × 1181
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 212,816,736
Proper Divisor Sum 144,507,696
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #68308969 ← → #68309041

Radix Representation

Decimal 68309040
Binary 100000100100101000000110000 (27 bits)
Octal 0o404450060
Hexadecimal 0x4125030

Divisor Catalog (60 of 80)

1 2 3 4 5 6 8 10 12 15 16 20 24 30 40 48 60 80 120 240 241 482 723 964 1,181 1,205 1,446 1,928 2,362 2,410 2,892 3,543 3,615 3,856 4,724 4,820 5,784 5,905 7,086 7,230 9,448 9,640 11,568 11,810 14,172 14,460 17,715 18,896 19,280 23,620 28,344 28,920 35,430 47,240 56,688 57,840 70,860 94,480 141,720 283,440

Collatz Trajectory (215 steps to reach 1)

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

68,309,040 34,154,520 17,077,260 8,538,630 4,269,315 12,807,946 6,403,973 19,211,920 9,605,960 4,802,980 2,401,490 1,200,745 3,602,236 1,801,118 900,559 2,701,678 1,350,839 4,052,518 2,026,259 6,078,778 3,039,389 9,118,168 4,559,084 2,279,542 1,139,771 3,419,314 1,709,657 5,128,972 2,564,486 1,282,243 3,846,730 1,923,365 5,770,096 2,885,048 1,442,524 721,262 360,631 1,081,894 540,947 1,622,842 811,421 2,434,264 1,217,132 608,566 304,283 912,850 456,425 1,369,276 684,638 342,319 1,026,958 513,479 1,540,438 770,219 2,310,658 1,155,329 3,465,988 1,732,994 866,497 2,599,492

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