612,720

2⁴ × 3² × 5 × 23 × 37

612,720 factors as 2^4 × 3^2 × 5 × 23 × 37. Its 120 positive divisors give a proper-divisor sum of 1,592,496, so this integer is abundant. The Collatz stopping time is 159 steps.

Prime Factor Structure

Factorization String 2^4 × 3^2 × 5 × 23 × 37

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 120

Divisor Sum (σ) 2,205,216

Proper Divisor Sum 1,592,496

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #612719 ← → #612727

Radix Representation

Decimal	612720
Binary	10010101100101110000 (20 bits)
Octal	0o2254560
Hexadecimal	0x95970

Divisor Catalog (60 of 120)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 23 24 30 36 37 40 45 46 48 60 69 72 74 80 90 92 111 115 120 138 144 148 180 184 185 207 222 230 240 276 296 333 345 360 368 370 414 444 460 552 555 592 666 690 720 740

Collatz Trajectory (159 steps to reach 1)

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

612,720 306,360 153,180 76,590 38,295 114,886 57,443 172,330 86,165 258,496 129,248 64,624 32,312 16,156 8,078 4,039 12,118 6,059 18,178 9,089 27,268 13,634 6,817 20,452 10,226 5,113 15,340 7,670 3,835 11,506 5,753 17,260 8,630 4,315 12,946 6,473 19,420 9,710 4,855 14,566 7,283 21,850 10,925 32,776 16,388 8,194 4,097 12,292 6,146 3,073 9,220 4,610 2,305 6,916 3,458 1,729 5,188 2,594 1,297 3,892

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