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Atlas › Integer Profiles › Node 10,072,764

10,072,764

22 × 32 × 13 × 21523
Abundant Even Composite

10,072,764 factors as 2^2 × 3^2 × 13 × 21523. Its 36 positive divisors give a proper-divisor sum of 17,348,812, so this integer is abundant. The Collatz stopping time is 145 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 13 × 21523
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 27,421,576
Proper Divisor Sum 17,348,812
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #10072729 ← → #10072817

Radix Representation

Decimal 10072764
Binary 100110011011001010111100 (24 bits)
Octal 0o46331274
Hexadecimal 0x99B2BC

Divisor Catalog (36)

1 2 3 4 6 9 12 13 18 26 36 39 52 78 117 156 234 468 21,523 43,046 64,569 86,092 129,138 193,707 258,276 279,799 387,414 559,598 774,828 839,397 1,119,196 1,678,794 2,518,191 3,357,588 5,036,382 10,072,764

Collatz Trajectory (145 steps to reach 1)

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

10,072,764 5,036,382 2,518,191 7,554,574 3,777,287 11,331,862 5,665,931 16,997,794 8,498,897 25,496,692 12,748,346 6,374,173 19,122,520 9,561,260 4,780,630 2,390,315 7,170,946 3,585,473 10,756,420 5,378,210 2,689,105 8,067,316 4,033,658 2,016,829 6,050,488 3,025,244 1,512,622 756,311 2,268,934 1,134,467 3,403,402 1,701,701 5,105,104 2,552,552 1,276,276 638,138 319,069 957,208 478,604 239,302 119,651 358,954 179,477 538,432 269,216 134,608 67,304 33,652 16,826 8,413 25,240 12,620 6,310 3,155 9,466 4,733 14,200 7,100 3,550 1,775

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