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Atlas › Integer Profiles › Node 48,759,744

48,759,744

26 × 3 × 11 × 23087
Abundant Even Composite

48,759,744 factors as 2^6 × 3 × 11 × 23087. Its 56 positive divisors give a proper-divisor sum of 91,984,704, so this integer is abundant. The Collatz stopping time is 85 steps.

Prime Factor Structure

Factorization String 2^6 × 3 × 11 × 23087
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 56
Divisor Sum (σ) 140,744,448
Proper Divisor Sum 91,984,704
Digit Sum / Digital Root 48 (Root: 3)
Adjacent Primes #48759743 ← → #48759751

Radix Representation

Decimal 48759744
Binary 10111010000000001111000000 (26 bits)
Octal 0o272001700
Hexadecimal 0x2E803C0

Divisor Catalog (56)

1 2 3 4 6 8 11 12 16 22 24 32 33 44 48 64 66 88 96 132 176 192 264 352 528 704 1,056 2,112 23,087 46,174 69,261 92,348 138,522 184,696 253,957 277,044 369,392 507,914 554,088 738,784 761,871 1,015,828 1,108,176 1,477,568 1,523,742 2,031,656 2,216,352 3,047,484 4,063,312 4,432,704 6,094,968 8,126,624 12,189,936 16,253,248 24,379,872 48,759,744

Collatz Trajectory (85 steps to reach 1)

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

48,759,744 24,379,872 12,189,936 6,094,968 3,047,484 1,523,742 761,871 2,285,614 1,142,807 3,428,422 1,714,211 5,142,634 2,571,317 7,713,952 3,856,976 1,928,488 964,244 482,122 241,061 723,184 361,592 180,796 90,398 45,199 135,598 67,799 203,398 101,699 305,098 152,549 457,648 228,824 114,412 57,206 28,603 85,810 42,905 128,716 64,358 32,179 96,538 48,269 144,808 72,404 36,202 18,101 54,304 27,152 13,576 6,788 3,394 1,697 5,092 2,546 1,273 3,820 1,910 955 2,866 1,433

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