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Atlas › Integer Profiles › Node 83,045,032

83,045,032

23 × 7 × 31 × 47837
Abundant Even Composite

83,045,032 factors as 2^3 × 7 × 31 × 47837. Its 32 positive divisors give a proper-divisor sum of 100,652,888, so this integer is abundant. The Collatz stopping time is 47 steps.

Prime Factor Structure

Factorization String 2^3 × 7 × 31 × 47837
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 183,697,920
Proper Divisor Sum 100,652,888
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #83045023 ← → #83045033

Radix Representation

Decimal 83045032
Binary 100111100110010101010101000 (27 bits)
Octal 0o474625250
Hexadecimal 0x4F32AA8

Divisor Catalog (32)

1 2 4 7 8 14 28 31 56 62 124 217 248 434 868 1,736 47,837 95,674 191,348 334,859 382,696 669,718 1,339,436 1,482,947 2,678,872 2,965,894 5,931,788 10,380,629 11,863,576 20,761,258 41,522,516 83,045,032

Collatz Trajectory (47 steps to reach 1)

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

83,045,032 41,522,516 20,761,258 10,380,629 31,141,888 15,570,944 7,785,472 3,892,736 1,946,368 973,184 486,592 243,296 121,648 60,824 30,412 15,206 7,603 22,810 11,405 34,216 17,108 8,554 4,277 12,832 6,416 3,208 1,604 802 401 1,204 602 301 904 452 226 113 340 170 85 256 128 64 32 16 8 4 2 1

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