722,796

2² × 3 × 29 × 31 × 67

722,796 factors as 2^2 × 3 × 29 × 31 × 67. Its 48 positive divisors give a proper-divisor sum of 1,105,044, so this integer is abundant. The Collatz stopping time is 167 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 29 × 31 × 67

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,827,840

Proper Divisor Sum 1,105,044

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #722791 ← → #722797

Radix Representation

Decimal	722796
Binary	10110000011101101100 (20 bits)
Octal	0o2603554
Hexadecimal	0xB076C

Divisor Catalog (48)

1 2 3 4 6 12 29 31 58 62 67 87 93 116 124 134 174 186 201 268 348 372 402 804 899 1,798 1,943 2,077 2,697 3,596 3,886 4,154 5,394 5,829 6,231 7,772 8,308 10,788 11,658 12,462 23,316 24,924 60,233 120,466 180,699 240,932 361,398 722,796

Collatz Trajectory (167 steps to reach 1)

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

722,796 361,398 180,699 542,098 271,049 813,148 406,574 203,287 609,862 304,931 914,794 457,397 1,372,192 686,096 343,048 171,524 85,762 42,881 128,644 64,322 32,161 96,484 48,242 24,121 72,364 36,182 18,091 54,274 27,137 81,412 40,706 20,353 61,060 30,530 15,265 45,796 22,898 11,449 34,348 17,174 8,587 25,762 12,881 38,644 19,322 9,661 28,984 14,492 7,246 3,623 10,870 5,435 16,306 8,153 24,460 12,230 6,115 18,346 9,173 27,520

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