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Atlas › Integer Profiles › Node 88,508,320

88,508,320

25 × 5 × 101 × 5477
Abundant Even Composite

88,508,320 factors as 2^5 × 5 × 101 × 5477. Its 48 positive divisors give a proper-divisor sum of 122,701,448, so this integer is abundant. The Collatz stopping time is 205 steps.

Prime Factor Structure

Factorization String 2^5 × 5 × 101 × 5477
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 211,209,768
Proper Divisor Sum 122,701,448
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #88508309 ← → #88508333

Radix Representation

Decimal 88508320
Binary 101010001101000011110100000 (27 bits)
Octal 0o521503640
Hexadecimal 0x54687A0

Divisor Catalog (48)

1 2 4 5 8 10 16 20 32 40 80 101 160 202 404 505 808 1,010 1,616 2,020 3,232 4,040 5,477 8,080 10,954 16,160 21,908 27,385 43,816 54,770 87,632 109,540 175,264 219,080 438,160 553,177 876,320 1,106,354 2,212,708 2,765,885 4,425,416 5,531,770 8,850,832 11,063,540 17,701,664 22,127,080 44,254,160 88,508,320

Collatz Trajectory (205 steps to reach 1)

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

88,508,320 44,254,160 22,127,080 11,063,540 5,531,770 2,765,885 8,297,656 4,148,828 2,074,414 1,037,207 3,111,622 1,555,811 4,667,434 2,333,717 7,001,152 3,500,576 1,750,288 875,144 437,572 218,786 109,393 328,180 164,090 82,045 246,136 123,068 61,534 30,767 92,302 46,151 138,454 69,227 207,682 103,841 311,524 155,762 77,881 233,644 116,822 58,411 175,234 87,617 262,852 131,426 65,713 197,140 98,570 49,285 147,856 73,928 36,964 18,482 9,241 27,724 13,862 6,931 20,794 10,397 31,192 15,596

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