742,800

2⁴ × 3 × 5² × 619

742,800 has digital root 3. The neighboring primes are 742789 and 742801; its proper-divisor sum differs from the starting integer by 897,680.

Prime Factor Structure

Factorization String 2^4 × 3 × 5^2 × 619

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 60

Divisor Sum (σ) 2,383,280

Proper Divisor Sum 1,640,480

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #742789 ← → #742801

Radix Representation

Decimal	742800
Binary	10110101010110010000 (20 bits)
Octal	0o2652620
Hexadecimal	0xB5590

Divisor Catalog (60)

1 2 3 4 5 6 8 10 12 15 16 20 24 25 30 40 48 50 60 75 80 100 120 150 200 240 300 400 600 619 1,200 1,238 1,857 2,476 3,095 3,714 4,952 6,190 7,428 9,285 9,904 12,380 14,856 15,475 18,570 24,760 29,712 30,950 37,140 46,425 49,520 61,900 74,280 92,850 123,800 148,560 185,700 247,600 371,400 742,800

Collatz Trajectory (180 steps to reach 1)

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

742,800 371,400 185,700 92,850 46,425 139,276 69,638 34,819 104,458 52,229 156,688 78,344 39,172 19,586 9,793 29,380 14,690 7,345 22,036 11,018 5,509 16,528 8,264 4,132 2,066 1,033 3,100 1,550 775 2,326 1,163 3,490 1,745 5,236 2,618 1,309 3,928 1,964 982 491 1,474 737 2,212 1,106 553 1,660 830 415 1,246 623 1,870 935 2,806 1,403 4,210 2,105 6,316 3,158 1,579 4,738

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