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Atlas › Integer Profiles › Node 33,837,280

33,837,280

25 × 5 × 79 × 2677
Abundant Even Composite

33,837,280 factors as 2^5 × 5 × 79 × 2677. Its 48 positive divisors give a proper-divisor sum of 47,145,440, so this integer is abundant. The Collatz stopping time is 82 steps.

Prime Factor Structure

Factorization String 2^5 × 5 × 79 × 2677
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 80,982,720
Proper Divisor Sum 47,145,440
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #33837263 ← → #33837283

Radix Representation

Decimal 33837280
Binary 10000001000101000011100000 (26 bits)
Octal 0o201050340
Hexadecimal 0x20450E0

Divisor Catalog (48)

1 2 4 5 8 10 16 20 32 40 79 80 158 160 316 395 632 790 1,264 1,580 2,528 2,677 3,160 5,354 6,320 10,708 12,640 13,385 21,416 26,770 42,832 53,540 85,664 107,080 211,483 214,160 422,966 428,320 845,932 1,057,415 1,691,864 2,114,830 3,383,728 4,229,660 6,767,456 8,459,320 16,918,640 33,837,280

Collatz Trajectory (82 steps to reach 1)

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

33,837,280 16,918,640 8,459,320 4,229,660 2,114,830 1,057,415 3,172,246 1,586,123 4,758,370 2,379,185 7,137,556 3,568,778 1,784,389 5,353,168 2,676,584 1,338,292 669,146 334,573 1,003,720 501,860 250,930 125,465 376,396 188,198 94,099 282,298 141,149 423,448 211,724 105,862 52,931 158,794 79,397 238,192 119,096 59,548 29,774 14,887 44,662 22,331 66,994 33,497 100,492 50,246 25,123 75,370 37,685 113,056 56,528 28,264 14,132 7,066 3,533 10,600 5,300 2,650 1,325 3,976 1,988 994

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