721,000

2³ × 5³ × 7 × 103

721,000 factors as 2^3 × 5^3 × 7 × 103. Its 64 positive divisors give a proper-divisor sum of 1,225,880, so this integer is abundant. The Collatz stopping time is 66 steps.

Prime Factor Structure

Factorization String 2^3 × 5^3 × 7 × 103

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 1,946,880

Proper Divisor Sum 1,225,880

Digit Sum / Digital Root 10 (Root: 1)

Adjacent Primes #720997 ← → #721003

Radix Representation

Decimal	721000
Binary	10110000000001101000 (20 bits)
Octal	0o2600150
Hexadecimal	0xB0068

Divisor Catalog (60 of 64)

1 2 4 5 7 8 10 14 20 25 28 35 40 50 56 70 100 103 125 140 175 200 206 250 280 350 412 500 515 700 721 824 875 1,000 1,030 1,400 1,442 1,750 2,060 2,575 2,884 3,500 3,605 4,120 5,150 5,768 7,000 7,210 10,300 12,875 14,420 18,025 20,600 25,750 28,840 36,050 51,500 72,100 90,125 103,000

Collatz Trajectory (66 steps to reach 1)

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

721,000 360,500 180,250 90,125 270,376 135,188 67,594 33,797 101,392 50,696 25,348 12,674 6,337 19,012 9,506 4,753 14,260 7,130 3,565 10,696 5,348 2,674 1,337 4,012 2,006 1,003 3,010 1,505 4,516 2,258 1,129 3,388 1,694 847 2,542 1,271 3,814 1,907 5,722 2,861 8,584 4,292 2,146 1,073 3,220 1,610 805 2,416 1,208 604 302 151 454 227 682 341 1,024 512 256 128

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