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Atlas › Integer Profiles › Node 77,260,432

77,260,432

24 × 31 × 53 × 2939
Abundant Even Composite

77,260,432 factors as 2^4 × 31 × 53 × 2939. Its 40 positive divisors give a proper-divisor sum of 80,229,488, so this integer is abundant. The Collatz stopping time is 122 steps.

Prime Factor Structure

Factorization String 2^4 × 31 × 53 × 2939
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 157,489,920
Proper Divisor Sum 80,229,488
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #77260429 ← → #77260453

Radix Representation

Decimal 77260432
Binary 100100110101110011010010000 (27 bits)
Octal 0o446563220
Hexadecimal 0x49AE690

Divisor Catalog (40)

1 2 4 8 16 31 53 62 106 124 212 248 424 496 848 1,643 2,939 3,286 5,878 6,572 11,756 13,144 23,512 26,288 47,024 91,109 155,767 182,218 311,534 364,436 623,068 728,872 1,246,136 1,457,744 2,492,272 4,828,777 9,657,554 19,315,108 38,630,216 77,260,432

Collatz Trajectory (122 steps to reach 1)

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

77,260,432 38,630,216 19,315,108 9,657,554 4,828,777 14,486,332 7,243,166 3,621,583 10,864,750 5,432,375 16,297,126 8,148,563 24,445,690 12,222,845 36,668,536 18,334,268 9,167,134 4,583,567 13,750,702 6,875,351 20,626,054 10,313,027 30,939,082 15,469,541 46,408,624 23,204,312 11,602,156 5,801,078 2,900,539 8,701,618 4,350,809 13,052,428 6,526,214 3,263,107 9,789,322 4,894,661 14,683,984 7,341,992 3,670,996 1,835,498 917,749 2,753,248 1,376,624 688,312 344,156 172,078 86,039 258,118 129,059 387,178 193,589 580,768 290,384 145,192 72,596 36,298 18,149 54,448 27,224 13,612

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