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Atlas › Integer Profiles › Node 46,872,012

46,872,012

22 × 3 × 112 × 19 × 1699
Abundant Even Composite

46,872,012 factors as 2^2 × 3 × 11^2 × 19 × 1699. Its 72 positive divisors give a proper-divisor sum of 79,743,988, so this integer is abundant. The Collatz stopping time is 248 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 11^2 × 19 × 1699
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 126,616,000
Proper Divisor Sum 79,743,988
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #46872011 ← → #46872029

Radix Representation

Decimal 46872012
Binary 10110010110011010111001100 (26 bits)
Octal 0o262632714
Hexadecimal 0x2CB35CC

Divisor Catalog (60 of 72)

1 2 3 4 6 11 12 19 22 33 38 44 57 66 76 114 121 132 209 228 242 363 418 484 627 726 836 1,254 1,452 1,699 2,299 2,508 3,398 4,598 5,097 6,796 6,897 9,196 10,194 13,794 18,689 20,388 27,588 32,281 37,378 56,067 64,562 74,756 96,843 112,134 129,124 193,686 205,579 224,268 355,091 387,372 411,158 616,737 710,182 822,316

Collatz Trajectory (248 steps to reach 1)

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

46,872,012 23,436,006 11,718,003 35,154,010 17,577,005 52,731,016 26,365,508 13,182,754 6,591,377 19,774,132 9,887,066 4,943,533 14,830,600 7,415,300 3,707,650 1,853,825 5,561,476 2,780,738 1,390,369 4,171,108 2,085,554 1,042,777 3,128,332 1,564,166 782,083 2,346,250 1,173,125 3,519,376 1,759,688 879,844 439,922 219,961 659,884 329,942 164,971 494,914 247,457 742,372 371,186 185,593 556,780 278,390 139,195 417,586 208,793 626,380 313,190 156,595 469,786 234,893 704,680 352,340 176,170 88,085 264,256 132,128 66,064 33,032 16,516 8,258

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