λ
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720,072

23 × 32 × 73 × 137
Abundant Even Composite

720,072 factors as 2^3 × 3^2 × 73 × 137. Its 48 positive divisors give a proper-divisor sum of 1,271,268, so this integer is abundant. The Collatz stopping time is 92 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 73 × 137
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 1,991,340
Proper Divisor Sum 1,271,268
Digit Sum / Digital Root 18 (Root: 9)
Adjacent Primes #720059 ← → #720089

Radix Representation

Decimal 720072
Binary 10101111110011001000 (20 bits)
Octal 0o2576310
Hexadecimal 0xAFCC8

Divisor Catalog (48)

1 2 3 4 6 8 9 12 18 24 36 72 73 137 146 219 274 292 411 438 548 584 657 822 876 1,096 1,233 1,314 1,644 1,752 2,466 2,628 3,288 4,932 5,256 9,864 10,001 20,002 30,003 40,004 60,006 80,008 90,009 120,012 180,018 240,024 360,036 720,072

Collatz Trajectory (92 steps to reach 1)

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

720,072 360,036 180,018 90,009 270,028 135,014 67,507 202,522 101,261 303,784 151,892 75,946 37,973 113,920 56,960 28,480 14,240 7,120 3,560 1,780 890 445 1,336 668 334 167 502 251 754 377 1,132 566 283 850 425 1,276 638 319 958 479 1,438 719 2,158 1,079 3,238 1,619 4,858 2,429 7,288 3,644 1,822 911 2,734 1,367 4,102 2,051 6,154 3,077 9,232 4,616

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