λ
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Atlas › Integer Profiles › Node 37,122,100

37,122,100

22 × 52 × 37 × 79 × 127
Abundant Even Composite

37,122,100 factors as 2^2 × 5^2 × 37 × 79 × 127. Its 72 positive divisors give a proper-divisor sum of 47,316,940, so this integer is abundant. The Collatz stopping time is 90 steps.

Prime Factor Structure

Factorization String 2^2 × 5^2 × 37 × 79 × 127
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 84,439,040
Proper Divisor Sum 47,316,940
Digit Sum / Digital Root 16 (Root: 7)
Adjacent Primes #37122077 ← → #37122103

Radix Representation

Decimal 37122100
Binary 10001101100111000000110100 (26 bits)
Octal 0o215470064
Hexadecimal 0x2367034

Divisor Catalog (60 of 72)

1 2 4 5 10 20 25 37 50 74 79 100 127 148 158 185 254 316 370 395 508 635 740 790 925 1,270 1,580 1,850 1,975 2,540 2,923 3,175 3,700 3,950 4,699 5,846 6,350 7,900 9,398 10,033 11,692 12,700 14,615 18,796 20,066 23,495 29,230 40,132 46,990 50,165 58,460 73,075 93,980 100,330 117,475 146,150 200,660 234,950 250,825 292,300

Collatz Trajectory (90 steps to reach 1)

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

37,122,100 18,561,050 9,280,525 27,841,576 13,920,788 6,960,394 3,480,197 10,440,592 5,220,296 2,610,148 1,305,074 652,537 1,957,612 978,806 489,403 1,468,210 734,105 2,202,316 1,101,158 550,579 1,651,738 825,869 2,477,608 1,238,804 619,402 309,701 929,104 464,552 232,276 116,138 58,069 174,208 87,104 43,552 21,776 10,888 5,444 2,722 1,361 4,084 2,042 1,021 3,064 1,532 766 383 1,150 575 1,726 863 2,590 1,295 3,886 1,943 5,830 2,915 8,746 4,373 13,120 6,560

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