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Atlas › Integer Profiles › Node 71,010,100

71,010,100

22 × 52 × 7 × 61 × 1663
Abundant Even Composite

71,010,100 factors as 2^2 × 5^2 × 7 × 61 × 1663. Its 72 positive divisors give a proper-divisor sum of 108,089,548, so this integer is abundant. The Collatz stopping time is 290 steps.

Prime Factor Structure

Factorization String 2^2 × 5^2 × 7 × 61 × 1663
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 179,099,648
Proper Divisor Sum 108,089,548
Digit Sum / Digital Root 10 (Root: 1)
Adjacent Primes #71010083 ← → #71010103

Radix Representation

Decimal 71010100
Binary 100001110111000011100110100 (27 bits)
Octal 0o416703464
Hexadecimal 0x43B8734

Divisor Catalog (60 of 72)

1 2 4 5 7 10 14 20 25 28 35 50 61 70 100 122 140 175 244 305 350 427 610 700 854 1,220 1,525 1,663 1,708 2,135 3,050 3,326 4,270 6,100 6,652 8,315 8,540 10,675 11,641 16,630 21,350 23,282 33,260 41,575 42,700 46,564 58,205 83,150 101,443 116,410 166,300 202,886 232,820 291,025 405,772 507,215 582,050 710,101 1,014,430 1,164,100

Collatz Trajectory (290 steps to reach 1)

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

71,010,100 35,505,050 17,752,525 53,257,576 26,628,788 13,314,394 6,657,197 19,971,592 9,985,796 4,992,898 2,496,449 7,489,348 3,744,674 1,872,337 5,617,012 2,808,506 1,404,253 4,212,760 2,106,380 1,053,190 526,595 1,579,786 789,893 2,369,680 1,184,840 592,420 296,210 148,105 444,316 222,158 111,079 333,238 166,619 499,858 249,929 749,788 374,894 187,447 562,342 281,171 843,514 421,757 1,265,272 632,636 316,318 158,159 474,478 237,239 711,718 355,859 1,067,578 533,789 1,601,368 800,684 400,342 200,171 600,514 300,257 900,772 450,386

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