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Atlas › Integer Profiles › Node 21,396,830

21,396,830

2 × 5 × 72 × 13 × 3359
Abundant Even Composite

21,396,830 factors as 2 × 5 × 7^2 × 13 × 3359. Its 48 positive divisors give a proper-divisor sum of 26,866,210, so this integer is abundant. The Collatz stopping time is 159 steps.

Prime Factor Structure

Factorization String 2 × 5 × 7^2 × 13 × 3359
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 48,263,040
Proper Divisor Sum 26,866,210
Digit Sum / Digital Root 32 (Root: 5)
Adjacent Primes #21396827 ← → #21396853

Radix Representation

Decimal 21396830
Binary 1010001100111110101011110 (25 bits)
Octal 0o121476536
Hexadecimal 0x1467D5E

Divisor Catalog (48)

1 2 5 7 10 13 14 26 35 49 65 70 91 98 130 182 245 455 490 637 910 1,274 3,185 3,359 6,370 6,718 16,795 23,513 33,590 43,667 47,026 87,334 117,565 164,591 218,335 235,130 305,669 329,182 436,670 611,338 822,955 1,528,345 1,645,910 2,139,683 3,056,690 4,279,366 10,698,415 21,396,830

Collatz Trajectory (159 steps to reach 1)

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

21,396,830 10,698,415 32,095,246 16,047,623 48,142,870 24,071,435 72,214,306 36,107,153 108,321,460 54,160,730 27,080,365 81,241,096 40,620,548 20,310,274 10,155,137 30,465,412 15,232,706 7,616,353 22,849,060 11,424,530 5,712,265 17,136,796 8,568,398 4,284,199 12,852,598 6,426,299 19,278,898 9,639,449 28,918,348 14,459,174 7,229,587 21,688,762 10,844,381 32,533,144 16,266,572 8,133,286 4,066,643 12,199,930 6,099,965 18,299,896 9,149,948 4,574,974 2,287,487 6,862,462 3,431,231 10,293,694 5,146,847 15,440,542 7,720,271 23,160,814 11,580,407 34,741,222 17,370,611 52,111,834 26,055,917 78,167,752 39,083,876 19,541,938 9,770,969 29,312,908

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