407,520

2⁵ × 3² × 5 × 283

407,520 factors as 2^5 × 3^2 × 5 × 283. Its 72 positive divisors give a proper-divisor sum of 988,056, so this integer is abundant. The Collatz stopping time is 99 steps.

Prime Factor Structure

Factorization String 2^5 × 3^2 × 5 × 283

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 1,395,576

Proper Divisor Sum 988,056

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #407509 ← → #407521

Radix Representation

Decimal	407520
Binary	1100011011111100000 (19 bits)
Octal	0o1433740
Hexadecimal	0x637E0

Divisor Catalog (60 of 72)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 32 36 40 45 48 60 72 80 90 96 120 144 160 180 240 283 288 360 480 566 720 849 1,132 1,415 1,440 1,698 2,264 2,547 2,830 3,396 4,245 4,528 5,094 5,660 6,792 8,490 9,056 10,188 11,320 12,735 13,584 16,980 20,376 22,640

Collatz Trajectory (99 steps to reach 1)

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

407,520 203,760 101,880 50,940 25,470 12,735 38,206 19,103 57,310 28,655 85,966 42,983 128,950 64,475 193,426 96,713 290,140 145,070 72,535 217,606 108,803 326,410 163,205 489,616 244,808 122,404 61,202 30,601 91,804 45,902 22,951 68,854 34,427 103,282 51,641 154,924 77,462 38,731 116,194 58,097 174,292 87,146 43,573 130,720 65,360 32,680 16,340 8,170 4,085 12,256 6,128 3,064 1,532 766 383 1,150 575 1,726 863 2,590

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