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Atlas › Integer Profiles › Node 734,320

734,320

24 × 5 × 67 × 137
Abundant Even Composite

734,320 factors as 2^4 × 5 × 67 × 137. Its 40 positive divisors give a proper-divisor sum of 1,011,104, so this integer is abundant. The Collatz stopping time is 211 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 67 × 137
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 1,745,424
Proper Divisor Sum 1,011,104
Digit Sum / Digital Root 19 (Root: 1)
Adjacent Primes #734303 ← → #734329

Radix Representation

Decimal 734320
Binary 10110011010001110000 (20 bits)
Octal 0o2632160
Hexadecimal 0xB3470

Divisor Catalog (40)

1 2 4 5 8 10 16 20 40 67 80 134 137 268 274 335 536 548 670 685 1,072 1,096 1,340 1,370 2,192 2,680 2,740 5,360 5,480 9,179 10,960 18,358 36,716 45,895 73,432 91,790 146,864 183,580 367,160 734,320

Collatz Trajectory (211 steps to reach 1)

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

734,320 367,160 183,580 91,790 45,895 137,686 68,843 206,530 103,265 309,796 154,898 77,449 232,348 116,174 58,087 174,262 87,131 261,394 130,697 392,092 196,046 98,023 294,070 147,035 441,106 220,553 661,660 330,830 165,415 496,246 248,123 744,370 372,185 1,116,556 558,278 279,139 837,418 418,709 1,256,128 628,064 314,032 157,016 78,508 39,254 19,627 58,882 29,441 88,324 44,162 22,081 66,244 33,122 16,561 49,684 24,842 12,421 37,264 18,632 9,316 4,658

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