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Atlas › Integer Profiles › Node 48,246,744

48,246,744

23 × 3 × 7 × 13 × 22091
Abundant Even Composite

48,246,744 factors as 2^3 × 3 × 7 × 13 × 22091. Its 64 positive divisors give a proper-divisor sum of 100,211,496, so this integer is abundant. The Collatz stopping time is 186 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 7 × 13 × 22091
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 148,458,240
Proper Divisor Sum 100,211,496
Digit Sum / Digital Root 39 (Root: 3)
Adjacent Primes #48246743 ← → #48246763

Radix Representation

Decimal 48246744
Binary 10111000000010111111011000 (26 bits)
Octal 0o270027730
Hexadecimal 0x2E02FD8

Divisor Catalog (60 of 64)

1 2 3 4 6 7 8 12 13 14 21 24 26 28 39 42 52 56 78 84 91 104 156 168 182 273 312 364 546 728 1,092 2,184 22,091 44,182 66,273 88,364 132,546 154,637 176,728 265,092 287,183 309,274 463,911 530,184 574,366 618,548 861,549 927,822 1,148,732 1,237,096 1,723,098 1,855,644 2,010,281 2,297,464 3,446,196 3,711,288 4,020,562 6,030,843 6,892,392 8,041,124

Collatz Trajectory (186 steps to reach 1)

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

48,246,744 24,123,372 12,061,686 6,030,843 18,092,530 9,046,265 27,138,796 13,569,398 6,784,699 20,354,098 10,177,049 30,531,148 15,265,574 7,632,787 22,898,362 11,449,181 34,347,544 17,173,772 8,586,886 4,293,443 12,880,330 6,440,165 19,320,496 9,660,248 4,830,124 2,415,062 1,207,531 3,622,594 1,811,297 5,433,892 2,716,946 1,358,473 4,075,420 2,037,710 1,018,855 3,056,566 1,528,283 4,584,850 2,292,425 6,877,276 3,438,638 1,719,319 5,157,958 2,578,979 7,736,938 3,868,469 11,605,408 5,802,704 2,901,352 1,450,676 725,338 362,669 1,088,008 544,004 272,002 136,001 408,004 204,002 102,001 306,004

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