748,512

2⁵ × 3² × 23 × 113

For 748,512, the 72 positive divisors have a total of 2,240,784. Removing 748,512 leaves 1,492,272, which gives the abundant classification.

Prime Factor Structure

Factorization String 2^5 × 3^2 × 23 × 113

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 2,240,784

Proper Divisor Sum 1,492,272

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #748499 ← → #748513

Radix Representation

Decimal	748512
Binary	10110110101111100000 (20 bits)
Octal	0o2665740
Hexadecimal	0xB6BE0

Divisor Catalog (60 of 72)

1 2 3 4 6 8 9 12 16 18 23 24 32 36 46 48 69 72 92 96 113 138 144 184 207 226 276 288 339 368 414 452 552 678 736 828 904 1,017 1,104 1,356 1,656 1,808 2,034 2,208 2,599 2,712 3,312 3,616 4,068 5,198 5,424 6,624 7,797 8,136 10,396 10,848 15,594 16,272 20,792 23,391

Collatz Trajectory (87 steps to reach 1)

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

748,512 374,256 187,128 93,564 46,782 23,391 70,174 35,087 105,262 52,631 157,894 78,947 236,842 118,421 355,264 177,632 88,816 44,408 22,204 11,102 5,551 16,654 8,327 24,982 12,491 37,474 18,737 56,212 28,106 14,053 42,160 21,080 10,540 5,270 2,635 7,906 3,953 11,860 5,930 2,965 8,896 4,448 2,224 1,112 556 278 139 418 209 628 314 157 472 236 118 59 178 89 268 134

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