73,332

2² × 3³ × 7 × 97

73,332 factors as 2^2 × 3^3 × 7 × 97. Its 48 positive divisors give a proper-divisor sum of 146,188, so this integer is abundant. The Collatz stopping time is 94 steps.

Prime Factor Structure

Factorization String 2^2 × 3^3 × 7 × 97

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 219,520

Proper Divisor Sum 146,188

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #73331 ← → #73351

Radix Representation

Decimal	73332
Binary	10001111001110100 (17 bits)
Octal	0o217164
Hexadecimal	0x11E74

Divisor Catalog (48)

1 2 3 4 6 7 9 12 14 18 21 27 28 36 42 54 63 84 97 108 126 189 194 252 291 378 388 582 679 756 873 1,164 1,358 1,746 2,037 2,619 2,716 3,492 4,074 5,238 6,111 8,148 10,476 12,222 18,333 24,444 36,666 73,332

Collatz Trajectory (94 steps to reach 1)

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

73,332 36,666 18,333 55,000 27,500 13,750 6,875 20,626 10,313 30,940 15,470 7,735 23,206 11,603 34,810 17,405 52,216 26,108 13,054 6,527 19,582 9,791 29,374 14,687 44,062 22,031 66,094 33,047 99,142 49,571 148,714 74,357 223,072 111,536 55,768 27,884 13,942 6,971 20,914 10,457 31,372 15,686 7,843 23,530 11,765 35,296 17,648 8,824 4,412 2,206 1,103 3,310 1,655 4,966 2,483 7,450 3,725 11,176 5,588 2,794

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