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Atlas › Integer Profiles › Node 48,753,952

48,753,952

25 × 13 × 163 × 719
Abundant Even Composite

48,753,952 factors as 2^5 × 13 × 163 × 719. Its 48 positive divisors give a proper-divisor sum of 55,392,608, so this integer is abundant. The Collatz stopping time is 93 steps.

Prime Factor Structure

Factorization String 2^5 × 13 × 163 × 719
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 104,146,560
Proper Divisor Sum 55,392,608
Digit Sum / Digital Root 43 (Root: 7)
Adjacent Primes #48753941 ← → #48753953

Radix Representation

Decimal 48753952
Binary 10111001111110110100100000 (26 bits)
Octal 0o271766440
Hexadecimal 0x2E7ED20

Divisor Catalog (48)

1 2 4 8 13 16 26 32 52 104 163 208 326 416 652 719 1,304 1,438 2,119 2,608 2,876 4,238 5,216 5,752 8,476 9,347 11,504 16,952 18,694 23,008 33,904 37,388 67,808 74,776 117,197 149,552 234,394 299,104 468,788 937,576 1,523,561 1,875,152 3,047,122 3,750,304 6,094,244 12,188,488 24,376,976 48,753,952

Collatz Trajectory (93 steps to reach 1)

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

48,753,952 24,376,976 12,188,488 6,094,244 3,047,122 1,523,561 4,570,684 2,285,342 1,142,671 3,428,014 1,714,007 5,142,022 2,571,011 7,713,034 3,856,517 11,569,552 5,784,776 2,892,388 1,446,194 723,097 2,169,292 1,084,646 542,323 1,626,970 813,485 2,440,456 1,220,228 610,114 305,057 915,172 457,586 228,793 686,380 343,190 171,595 514,786 257,393 772,180 386,090 193,045 579,136 289,568 144,784 72,392 36,196 18,098 9,049 27,148 13,574 6,787 20,362 10,181 30,544 15,272 7,636 3,818 1,909 5,728 2,864 1,432

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