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Atlas › Integer Profiles › Node 83,036,742

83,036,742

2 × 3 × 79 × 167 × 1049
Abundant Even Composite

83,036,742 factors as 2 × 3 × 79 × 167 × 1049. Its 32 positive divisors give a proper-divisor sum of 86,307,258, so this integer is abundant. The Collatz stopping time is 99 steps.

Prime Factor Structure

Factorization String 2 × 3 × 79 × 167 × 1049
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 169,344,000
Proper Divisor Sum 86,307,258
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #83036731 ← → #83036771

Radix Representation

Decimal 83036742
Binary 100111100110000101001000110 (27 bits)
Octal 0o474605106
Hexadecimal 0x4F30A46

Divisor Catalog (32)

1 2 3 6 79 158 167 237 334 474 501 1,002 1,049 2,098 3,147 6,294 13,193 26,386 39,579 79,158 82,871 165,742 175,183 248,613 350,366 497,226 525,549 1,051,098 13,839,457 27,678,914 41,518,371 83,036,742

Collatz Trajectory (99 steps to reach 1)

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

83,036,742 41,518,371 124,555,114 62,277,557 186,832,672 93,416,336 46,708,168 23,354,084 11,677,042 5,838,521 17,515,564 8,757,782 4,378,891 13,136,674 6,568,337 19,705,012 9,852,506 4,926,253 14,778,760 7,389,380 3,694,690 1,847,345 5,542,036 2,771,018 1,385,509 4,156,528 2,078,264 1,039,132 519,566 259,783 779,350 389,675 1,169,026 584,513 1,753,540 876,770 438,385 1,315,156 657,578 328,789 986,368 493,184 246,592 123,296 61,648 30,824 15,412 7,706 3,853 11,560 5,780 2,890 1,445 4,336 2,168 1,084 542 271 814 407

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