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Atlas › Integer Profiles › Node 78,490,240

78,490,240

27 × 5 × 29 × 4229
Abundant Even Composite

78,490,240 factors as 2^7 × 5 × 29 × 4229. Its 64 positive divisors give a proper-divisor sum of 115,666,760, so this integer is abundant. The Collatz stopping time is 47 steps.

Prime Factor Structure

Factorization String 2^7 × 5 × 29 × 4229
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 194,157,000
Proper Divisor Sum 115,666,760
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #78490219 ← → #78490259

Radix Representation

Decimal 78490240
Binary 100101011011010101010000000 (27 bits)
Octal 0o453325200
Hexadecimal 0x4ADAA80

Divisor Catalog (60 of 64)

1 2 4 5 8 10 16 20 29 32 40 58 64 80 116 128 145 160 232 290 320 464 580 640 928 1,160 1,856 2,320 3,712 4,229 4,640 8,458 9,280 16,916 18,560 21,145 33,832 42,290 67,664 84,580 122,641 135,328 169,160 245,282 270,656 338,320 490,564 541,312 613,205 676,640 981,128 1,226,410 1,353,280 1,962,256 2,452,820 2,706,560 3,924,512 4,905,640 7,849,024 9,811,280

Collatz Trajectory (47 steps to reach 1)

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

78,490,240 39,245,120 19,622,560 9,811,280 4,905,640 2,452,820 1,226,410 613,205 1,839,616 919,808 459,904 229,952 114,976 57,488 28,744 14,372 7,186 3,593 10,780 5,390 2,695 8,086 4,043 12,130 6,065 18,196 9,098 4,549 13,648 6,824 3,412 1,706 853 2,560 1,280 640 320 160 80 40 20 10 5 16 8 4 2 1

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