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Atlas › Integer Profiles › Node 31,879,960

31,879,960

23 × 5 × 7 × 41 × 2777
Abundant Even Composite

31,879,960 factors as 2^3 × 5 × 7 × 41 × 2777. Its 64 positive divisors give a proper-divisor sum of 52,126,760, so this integer is abundant. The Collatz stopping time is 95 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 7 × 41 × 2777
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 84,006,720
Proper Divisor Sum 52,126,760
Digit Sum / Digital Root 43 (Root: 7)
Adjacent Primes #31879957 ← → #31879963

Radix Representation

Decimal 31879960
Binary 1111001100111001100011000 (25 bits)
Octal 0o171471430
Hexadecimal 0x1E67318

Divisor Catalog (60 of 64)

1 2 4 5 7 8 10 14 20 28 35 40 41 56 70 82 140 164 205 280 287 328 410 574 820 1,148 1,435 1,640 2,296 2,777 2,870 5,554 5,740 11,108 11,480 13,885 19,439 22,216 27,770 38,878 55,540 77,756 97,195 111,080 113,857 155,512 194,390 227,714 388,780 455,428 569,285 777,560 796,999 910,856 1,138,570 1,593,998 2,277,140 3,187,996 3,984,995 4,554,280

Collatz Trajectory (95 steps to reach 1)

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

31,879,960 15,939,980 7,969,990 3,984,995 11,954,986 5,977,493 17,932,480 8,966,240 4,483,120 2,241,560 1,120,780 560,390 280,195 840,586 420,293 1,260,880 630,440 315,220 157,610 78,805 236,416 118,208 59,104 29,552 14,776 7,388 3,694 1,847 5,542 2,771 8,314 4,157 12,472 6,236 3,118 1,559 4,678 2,339 7,018 3,509 10,528 5,264 2,632 1,316 658 329 988 494 247 742 371 1,114 557 1,672 836 418 209 628 314 157

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