λ
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Atlas › Integer Profiles › Node 72,020,980

72,020,980

22 × 5 × 67 × 71 × 757
Abundant Even Composite

72,020,980 factors as 2^2 × 5 × 67 × 71 × 757. Its 48 positive divisors give a proper-divisor sum of 83,848,076, so this integer is abundant. The Collatz stopping time is 122 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 67 × 71 × 757
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 155,869,056
Proper Divisor Sum 83,848,076
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #72020957 ← → #72020983

Radix Representation

Decimal 72020980
Binary 100010010101111001111110100 (27 bits)
Octal 0o422571764
Hexadecimal 0x44AF3F4

Divisor Catalog (48)

1 2 4 5 10 20 67 71 134 142 268 284 335 355 670 710 757 1,340 1,420 1,514 3,028 3,785 4,757 7,570 9,514 15,140 19,028 23,785 47,570 50,719 53,747 95,140 101,438 107,494 202,876 214,988 253,595 268,735 507,190 537,470 1,014,380 1,074,940 3,601,049 7,202,098 14,404,196 18,005,245 36,010,490 72,020,980

Collatz Trajectory (122 steps to reach 1)

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

72,020,980 36,010,490 18,005,245 54,015,736 27,007,868 13,503,934 6,751,967 20,255,902 10,127,951 30,383,854 15,191,927 45,575,782 22,787,891 68,363,674 34,181,837 102,545,512 51,272,756 25,636,378 12,818,189 38,454,568 19,227,284 9,613,642 4,806,821 14,420,464 7,210,232 3,605,116 1,802,558 901,279 2,703,838 1,351,919 4,055,758 2,027,879 6,083,638 3,041,819 9,125,458 4,562,729 13,688,188 6,844,094 3,422,047 10,266,142 5,133,071 15,399,214 7,699,607 23,098,822 11,549,411 34,648,234 17,324,117 51,972,352 25,986,176 12,993,088 6,496,544 3,248,272 1,624,136 812,068 406,034 203,017 609,052 304,526 152,263 456,790

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