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Atlas › Integer Profiles › Node 77,004,970

77,004,970

2 × 5 × 72 × 41 × 3833
Abundant Even Composite

77,004,970 factors as 2 × 5 × 7^2 × 41 × 3833. Its 48 positive divisors give a proper-divisor sum of 88,209,758, so this integer is abundant. The Collatz stopping time is 241 steps.

Prime Factor Structure

Factorization String 2 × 5 × 7^2 × 41 × 3833
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 165,214,728
Proper Divisor Sum 88,209,758
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #77004953 ← → #77004973

Radix Representation

Decimal 77004970
Binary 100100101110000000010101010 (27 bits)
Octal 0o445600252
Hexadecimal 0x49700AA

Divisor Catalog (48)

1 2 5 7 10 14 35 41 49 70 82 98 205 245 287 410 490 574 1,435 2,009 2,870 3,833 4,018 7,666 10,045 19,165 20,090 26,831 38,330 53,662 134,155 157,153 187,817 268,310 314,306 375,634 785,765 939,085 1,100,071 1,571,530 1,878,170 2,200,142 5,500,355 7,700,497 11,000,710 15,400,994 38,502,485 77,004,970

Collatz Trajectory (241 steps to reach 1)

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

77,004,970 38,502,485 115,507,456 57,753,728 28,876,864 14,438,432 7,219,216 3,609,608 1,804,804 902,402 451,201 1,353,604 676,802 338,401 1,015,204 507,602 253,801 761,404 380,702 190,351 571,054 285,527 856,582 428,291 1,284,874 642,437 1,927,312 963,656 481,828 240,914 120,457 361,372 180,686 90,343 271,030 135,515 406,546 203,273 609,820 304,910 152,455 457,366 228,683 686,050 343,025 1,029,076 514,538 257,269 771,808 385,904 192,952 96,476 48,238 24,119 72,358 36,179 108,538 54,269 162,808 81,404

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