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Atlas › Integer Profiles › Node 37,104,928

37,104,928

25 × 7 × 151 × 1097
Abundant Even Composite

37,104,928 factors as 2^5 × 7 × 151 × 1097. Its 48 positive divisors give a proper-divisor sum of 47,010,656, so this integer is abundant. The Collatz stopping time is 165 steps.

Prime Factor Structure

Factorization String 2^5 × 7 × 151 × 1097
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 84,115,584
Proper Divisor Sum 47,010,656
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #37104919 ← → #37104937

Radix Representation

Decimal 37104928
Binary 10001101100010110100100000 (26 bits)
Octal 0o215426440
Hexadecimal 0x2362D20

Divisor Catalog (48)

1 2 4 7 8 14 16 28 32 56 112 151 224 302 604 1,057 1,097 1,208 2,114 2,194 2,416 4,228 4,388 4,832 7,679 8,456 8,776 15,358 16,912 17,552 30,716 33,824 35,104 61,432 122,864 165,647 245,728 331,294 662,588 1,159,529 1,325,176 2,319,058 2,650,352 4,638,116 5,300,704 9,276,232 18,552,464 37,104,928

Collatz Trajectory (165 steps to reach 1)

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

37,104,928 18,552,464 9,276,232 4,638,116 2,319,058 1,159,529 3,478,588 1,739,294 869,647 2,608,942 1,304,471 3,913,414 1,956,707 5,870,122 2,935,061 8,805,184 4,402,592 2,201,296 1,100,648 550,324 275,162 137,581 412,744 206,372 103,186 51,593 154,780 77,390 38,695 116,086 58,043 174,130 87,065 261,196 130,598 65,299 195,898 97,949 293,848 146,924 73,462 36,731 110,194 55,097 165,292 82,646 41,323 123,970 61,985 185,956 92,978 46,489 139,468 69,734 34,867 104,602 52,301 156,904 78,452 39,226

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