27,577,600

2⁸ × 5² × 31 × 139

27,577,600 factors as 2^8 × 5^2 × 31 × 139. Its 108 positive divisors give a proper-divisor sum of 43,390,080, so this integer is abundant. The Collatz stopping time is 100 steps.

Prime Factor Structure

Factorization String 2^8 × 5^2 × 31 × 139

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 108

Divisor Sum (σ) 70,967,680

Proper Divisor Sum 43,390,080

Digit Sum / Digital Root 34 (Root: 7)

Adjacent Primes #27577567 ← → #27577601

Radix Representation

Decimal	27577600
Binary	1101001001100110100000000 (25 bits)
Octal	0o151146400
Hexadecimal	0x1A4CD00

Divisor Catalog (60 of 108)

1 2 4 5 8 10 16 20 25 31 32 40 50 62 64 80 100 124 128 139 155 160 200 248 256 278 310 320 400 496 556 620 640 695 775 800 992 1,112 1,240 1,280 1,390 1,550 1,600 1,984 2,224 2,480 2,780 3,100 3,200 3,475 3,968 4,309 4,448 4,960 5,560 6,200 6,400 6,950 7,936 8,618

Collatz Trajectory (100 steps to reach 1)

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

27,577,600 13,788,800 6,894,400 3,447,200 1,723,600 861,800 430,900 215,450 107,725 323,176 161,588 80,794 40,397 121,192 60,596 30,298 15,149 45,448 22,724 11,362 5,681 17,044 8,522 4,261 12,784 6,392 3,196 1,598 799 2,398 1,199 3,598 1,799 5,398 2,699 8,098 4,049 12,148 6,074 3,037 9,112 4,556 2,278 1,139 3,418 1,709 5,128 2,564 1,282 641 1,924 962 481 1,444 722 361 1,084 542 271 814

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