21,728,200

2³ × 5² × 13 × 61 × 137

21,728,200 factors as 2^3 × 5^2 × 13 × 61 × 137. Its 96 positive divisors give a proper-divisor sum of 33,971,360, so this integer is abundant. The Collatz stopping time is 141 steps.

Prime Factor Structure

Factorization String 2^3 × 5^2 × 13 × 61 × 137

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 55,699,560

Proper Divisor Sum 33,971,360

Digit Sum / Digital Root 22 (Root: 4)

Adjacent Primes #21728197 ← → #21728233

Radix Representation

Decimal	21728200
Binary	1010010111000101111001000 (25 bits)
Octal	0o122705710
Hexadecimal	0x14B8BC8

Divisor Catalog (60 of 96)

1 2 4 5 8 10 13 20 25 26 40 50 52 61 65 100 104 122 130 137 200 244 260 274 305 325 488 520 548 610 650 685 793 1,096 1,220 1,300 1,370 1,525 1,586 1,781 2,440 2,600 2,740 3,050 3,172 3,425 3,562 3,965 5,480 6,100 6,344 6,850 7,124 7,930 8,357 8,905 12,200 13,700 14,248 15,860

Collatz Trajectory (141 steps to reach 1)

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

21,728,200 10,864,100 5,432,050 2,716,025 8,148,076 4,074,038 2,037,019 6,111,058 3,055,529 9,166,588 4,583,294 2,291,647 6,874,942 3,437,471 10,312,414 5,156,207 15,468,622 7,734,311 23,202,934 11,601,467 34,804,402 17,402,201 52,206,604 26,103,302 13,051,651 39,154,954 19,577,477 58,732,432 29,366,216 14,683,108 7,341,554 3,670,777 11,012,332 5,506,166 2,753,083 8,259,250 4,129,625 12,388,876 6,194,438 3,097,219 9,291,658 4,645,829 13,937,488 6,968,744 3,484,372 1,742,186 871,093 2,613,280 1,306,640 653,320 326,660 163,330 81,665 244,996 122,498 61,249 183,748 91,874 45,937 137,812

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