λ
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Atlas › Integer Profiles › Node 42,576,264

42,576,264

23 × 32 × 19 × 31123
Abundant Even Composite

42,576,264 factors as 2^3 × 3^2 × 19 × 31123. Its 48 positive divisors give a proper-divisor sum of 78,807,336, so this integer is abundant. The Collatz stopping time is 235 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 19 × 31123
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 121,383,600
Proper Divisor Sum 78,807,336
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #42576251 ← → #42576269

Radix Representation

Decimal 42576264
Binary 10100010011010100110001000 (26 bits)
Octal 0o242324610
Hexadecimal 0x289A988

Divisor Catalog (48)

1 2 3 4 6 8 9 12 18 19 24 36 38 57 72 76 114 152 171 228 342 456 684 1,368 31,123 62,246 93,369 124,492 186,738 248,984 280,107 373,476 560,214 591,337 746,952 1,120,428 1,182,674 1,774,011 2,240,856 2,365,348 3,548,022 4,730,696 5,322,033 7,096,044 10,644,066 14,192,088 21,288,132 42,576,264

Collatz Trajectory (235 steps to reach 1)

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

42,576,264 21,288,132 10,644,066 5,322,033 15,966,100 7,983,050 3,991,525 11,974,576 5,987,288 2,993,644 1,496,822 748,411 2,245,234 1,122,617 3,367,852 1,683,926 841,963 2,525,890 1,262,945 3,788,836 1,894,418 947,209 2,841,628 1,420,814 710,407 2,131,222 1,065,611 3,196,834 1,598,417 4,795,252 2,397,626 1,198,813 3,596,440 1,798,220 899,110 449,555 1,348,666 674,333 2,023,000 1,011,500 505,750 252,875 758,626 379,313 1,137,940 568,970 284,485 853,456 426,728 213,364 106,682 53,341 160,024 80,012 40,006 20,003 60,010 30,005 90,016 45,008

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