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Atlas › Integer Profiles › Node 37,213,752

37,213,752

23 × 3 × 433 × 3581
Abundant Even Composite

37,213,752 factors as 2^3 × 3 × 433 × 3581. Its 32 positive divisors give a proper-divisor sum of 56,061,528, so this integer is abundant. The Collatz stopping time is 165 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 433 × 3581
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 93,275,280
Proper Divisor Sum 56,061,528
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #37213751 ← → #37213763

Radix Representation

Decimal 37213752
Binary 10001101111101011000111000 (26 bits)
Octal 0o215753070
Hexadecimal 0x237D638

Divisor Catalog (32)

1 2 3 4 6 8 12 24 433 866 1,299 1,732 2,598 3,464 3,581 5,196 7,162 10,392 10,743 14,324 21,486 28,648 42,972 85,944 1,550,573 3,101,146 4,651,719 6,202,292 9,303,438 12,404,584 18,606,876 37,213,752

Collatz Trajectory (165 steps to reach 1)

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

37,213,752 18,606,876 9,303,438 4,651,719 13,955,158 6,977,579 20,932,738 10,466,369 31,399,108 15,699,554 7,849,777 23,549,332 11,774,666 5,887,333 17,662,000 8,831,000 4,415,500 2,207,750 1,103,875 3,311,626 1,655,813 4,967,440 2,483,720 1,241,860 620,930 310,465 931,396 465,698 232,849 698,548 349,274 174,637 523,912 261,956 130,978 65,489 196,468 98,234 49,117 147,352 73,676 36,838 18,419 55,258 27,629 82,888 41,444 20,722 10,361 31,084 15,542 7,771 23,314 11,657 34,972 17,486 8,743 26,230 13,115 39,346

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