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Atlas › Integer Profiles › Node 10,091,032

10,091,032

23 × 7 × 367 × 491
Abundant Even Composite

10,091,032 factors as 2^3 × 7 × 367 × 491. Its 32 positive divisors give a proper-divisor sum of 11,635,688, so this integer is abundant. The Collatz stopping time is 207 steps.

Prime Factor Structure

Factorization String 2^3 × 7 × 367 × 491
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 21,726,720
Proper Divisor Sum 11,635,688
Digit Sum / Digital Root 16 (Root: 7)
Adjacent Primes #10091023 ← → #10091069

Radix Representation

Decimal 10091032
Binary 100110011111101000011000 (24 bits)
Octal 0o46375030
Hexadecimal 0x99FA18

Divisor Catalog (32)

1 2 4 7 8 14 28 56 367 491 734 982 1,468 1,964 2,569 2,936 3,437 3,928 5,138 6,874 10,276 13,748 20,552 27,496 180,197 360,394 720,788 1,261,379 1,441,576 2,522,758 5,045,516 10,091,032

Collatz Trajectory (207 steps to reach 1)

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

10,091,032 5,045,516 2,522,758 1,261,379 3,784,138 1,892,069 5,676,208 2,838,104 1,419,052 709,526 354,763 1,064,290 532,145 1,596,436 798,218 399,109 1,197,328 598,664 299,332 149,666 74,833 224,500 112,250 56,125 168,376 84,188 42,094 21,047 63,142 31,571 94,714 47,357 142,072 71,036 35,518 17,759 53,278 26,639 79,918 39,959 119,878 59,939 179,818 89,909 269,728 134,864 67,432 33,716 16,858 8,429 25,288 12,644 6,322 3,161 9,484 4,742 2,371 7,114 3,557 10,672

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