414,090

2 × 3² × 5 × 43 × 107

414,090 factors as 2 × 3^2 × 5 × 43 × 107. Its 48 positive divisors give a proper-divisor sum of 697,878, so this integer is abundant. The Collatz stopping time is 187 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 5 × 43 × 107

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,111,968

Proper Divisor Sum 697,878

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #414083 ← → #414097

Radix Representation

Decimal	414090
Binary	1100101000110001010 (19 bits)
Octal	0o1450612
Hexadecimal	0x6518A

Divisor Catalog (48)

1 2 3 5 6 9 10 15 18 30 43 45 86 90 107 129 214 215 258 321 387 430 535 642 645 774 963 1,070 1,290 1,605 1,926 1,935 3,210 3,870 4,601 4,815 9,202 9,630 13,803 23,005 27,606 41,409 46,010 69,015 82,818 138,030 207,045 414,090

Collatz Trajectory (187 steps to reach 1)

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

414,090 207,045 621,136 310,568 155,284 77,642 38,821 116,464 58,232 29,116 14,558 7,279 21,838 10,919 32,758 16,379 49,138 24,569 73,708 36,854 18,427 55,282 27,641 82,924 41,462 20,731 62,194 31,097 93,292 46,646 23,323 69,970 34,985 104,956 52,478 26,239 78,718 39,359 118,078 59,039 177,118 88,559 265,678 132,839 398,518 199,259 597,778 298,889 896,668 448,334 224,167 672,502 336,251 1,008,754 504,377 1,513,132 756,566 378,283 1,134,850 567,425

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