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Atlas › Integer Profiles › Node 33,723,950

33,723,950

2 × 52 × 133 × 307
Abundant Even Composite

33,723,950 factors as 2 × 5^2 × 13^3 × 307. Its 48 positive divisors give a proper-divisor sum of 34,448,770, so this integer is abundant. The Collatz stopping time is 338 steps.

Prime Factor Structure

Factorization String 2 × 5^2 × 13^3 × 307
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 68,172,720
Proper Divisor Sum 34,448,770
Digit Sum / Digital Root 32 (Root: 5)
Adjacent Primes #33723947 ← → #33723967

Radix Representation

Decimal 33723950
Binary 10000000101001011000101110 (26 bits)
Octal 0o200513056
Hexadecimal 0x202962E

Divisor Catalog (48)

1 2 5 10 13 25 26 50 65 130 169 307 325 338 614 650 845 1,535 1,690 2,197 3,070 3,991 4,225 4,394 7,675 7,982 8,450 10,985 15,350 19,955 21,970 39,910 51,883 54,925 99,775 103,766 109,850 199,550 259,415 518,830 674,479 1,297,075 1,348,958 2,594,150 3,372,395 6,744,790 16,861,975 33,723,950

Collatz Trajectory (338 steps to reach 1)

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

33,723,950 16,861,975 50,585,926 25,292,963 75,878,890 37,939,445 113,818,336 56,909,168 28,454,584 14,227,292 7,113,646 3,556,823 10,670,470 5,335,235 16,005,706 8,002,853 24,008,560 12,004,280 6,002,140 3,001,070 1,500,535 4,501,606 2,250,803 6,752,410 3,376,205 10,128,616 5,064,308 2,532,154 1,266,077 3,798,232 1,899,116 949,558 474,779 1,424,338 712,169 2,136,508 1,068,254 534,127 1,602,382 801,191 2,403,574 1,201,787 3,605,362 1,802,681 5,408,044 2,704,022 1,352,011 4,056,034 2,028,017 6,084,052 3,042,026 1,521,013 4,563,040 2,281,520 1,140,760 570,380 285,190 142,595 427,786 213,893

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