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Atlas › Integer Profiles › Node 77,001,072

77,001,072

24 × 3 × 19 × 84431
Abundant Even Composite

77,001,072 factors as 2^4 × 3 × 19 × 84431. Its 40 positive divisors give a proper-divisor sum of 132,390,288, so this integer is abundant. The Collatz stopping time is 316 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 19 × 84431
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 209,391,360
Proper Divisor Sum 132,390,288
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #77001059 ← → #77001073

Radix Representation

Decimal 77001072
Binary 100100101101111000101110000 (27 bits)
Octal 0o445570560
Hexadecimal 0x496F170

Divisor Catalog (40)

1 2 3 4 6 8 12 16 19 24 38 48 57 76 114 152 228 304 456 912 84,431 168,862 253,293 337,724 506,586 675,448 1,013,172 1,350,896 1,604,189 2,026,344 3,208,378 4,052,688 4,812,567 6,416,756 9,625,134 12,833,512 19,250,268 25,667,024 38,500,536 77,001,072

Collatz Trajectory (316 steps to reach 1)

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

77,001,072 38,500,536 19,250,268 9,625,134 4,812,567 14,437,702 7,218,851 21,656,554 10,828,277 32,484,832 16,242,416 8,121,208 4,060,604 2,030,302 1,015,151 3,045,454 1,522,727 4,568,182 2,284,091 6,852,274 3,426,137 10,278,412 5,139,206 2,569,603 7,708,810 3,854,405 11,563,216 5,781,608 2,890,804 1,445,402 722,701 2,168,104 1,084,052 542,026 271,013 813,040 406,520 203,260 101,630 50,815 152,446 76,223 228,670 114,335 343,006 171,503 514,510 257,255 771,766 385,883 1,157,650 578,825 1,736,476 868,238 434,119 1,302,358 651,179 1,953,538 976,769 2,930,308

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