727,112

2³ × 97 × 937

727,112 factors as 2^3 × 97 × 937. Its 16 positive divisors give a proper-divisor sum of 651,748, so this integer is deficient. The Collatz stopping time is 149 steps.

Prime Factor Structure

Factorization String 2^3 × 97 × 937

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 1,378,860

Proper Divisor Sum 651,748

Digit Sum / Digital Root 20 (Root: 2)

Adjacent Primes #727079 ← → #727121

Radix Representation

Decimal	727112
Binary	10110001100001001000 (20 bits)
Octal	0o2614110
Hexadecimal	0xB1848

Divisor Catalog (16)

1 2 4 8 97 194 388 776 937 1,874 3,748 7,496 90,889 181,778 363,556 727,112

Collatz Trajectory (149 steps to reach 1)

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

727,112 363,556 181,778 90,889 272,668 136,334 68,167 204,502 102,251 306,754 153,377 460,132 230,066 115,033 345,100 172,550 86,275 258,826 129,413 388,240 194,120 97,060 48,530 24,265 72,796 36,398 18,199 54,598 27,299 81,898 40,949 122,848 61,424 30,712 15,356 7,678 3,839 11,518 5,759 17,278 8,639 25,918 12,959 38,878 19,439 58,318 29,159 87,478 43,739 131,218 65,609 196,828 98,414 49,207 147,622 73,811 221,434 110,717 332,152 166,076

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