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Atlas › Integer Profiles › Node 27,972,768

27,972,768

25 × 3 × 67 × 4349
Abundant Even Composite

27,972,768 factors as 2^5 × 3 × 67 × 4349. Its 48 positive divisors give a proper-divisor sum of 46,568,832, so this integer is abundant. The Collatz stopping time is 118 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 67 × 4349
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 74,541,600
Proper Divisor Sum 46,568,832
Digit Sum / Digital Root 48 (Root: 3)
Adjacent Primes #27972767 ← → #27972773

Radix Representation

Decimal 27972768
Binary 1101010101101010010100000 (25 bits)
Octal 0o152552240
Hexadecimal 0x1AAD4A0

Divisor Catalog (48)

1 2 3 4 6 8 12 16 24 32 48 67 96 134 201 268 402 536 804 1,072 1,608 2,144 3,216 4,349 6,432 8,698 13,047 17,396 26,094 34,792 52,188 69,584 104,376 139,168 208,752 291,383 417,504 582,766 874,149 1,165,532 1,748,298 2,331,064 3,496,596 4,662,128 6,993,192 9,324,256 13,986,384 27,972,768

Collatz Trajectory (118 steps to reach 1)

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

27,972,768 13,986,384 6,993,192 3,496,596 1,748,298 874,149 2,622,448 1,311,224 655,612 327,806 163,903 491,710 245,855 737,566 368,783 1,106,350 553,175 1,659,526 829,763 2,489,290 1,244,645 3,733,936 1,866,968 933,484 466,742 233,371 700,114 350,057 1,050,172 525,086 262,543 787,630 393,815 1,181,446 590,723 1,772,170 886,085 2,658,256 1,329,128 664,564 332,282 166,141 498,424 249,212 124,606 62,303 186,910 93,455 280,366 140,183 420,550 210,275 630,826 315,413 946,240 473,120 236,560 118,280 59,140 29,570

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