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Atlas › Integer Profiles › Node 76,779,296

76,779,296

25 × 11 × 59 × 3697
Abundant Even Composite

76,779,296 factors as 2^5 × 11 × 59 × 3697. Its 48 positive divisors give a proper-divisor sum of 90,961,984, so this integer is abundant. The Collatz stopping time is 122 steps.

Prime Factor Structure

Factorization String 2^5 × 11 × 59 × 3697
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 167,741,280
Proper Divisor Sum 90,961,984
Digit Sum / Digital Root 53 (Root: 8)
Adjacent Primes #76779289 ← → #76779301

Radix Representation

Decimal 76779296
Binary 100100100111000111100100000 (27 bits)
Octal 0o444707440
Hexadecimal 0x4938F20

Divisor Catalog (48)

1 2 4 8 11 16 22 32 44 59 88 118 176 236 352 472 649 944 1,298 1,888 2,596 3,697 5,192 7,394 10,384 14,788 20,768 29,576 40,667 59,152 81,334 118,304 162,668 218,123 325,336 436,246 650,672 872,492 1,301,344 1,744,984 2,399,353 3,489,968 4,798,706 6,979,936 9,597,412 19,194,824 38,389,648 76,779,296

Collatz Trajectory (122 steps to reach 1)

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

76,779,296 38,389,648 19,194,824 9,597,412 4,798,706 2,399,353 7,198,060 3,599,030 1,799,515 5,398,546 2,699,273 8,097,820 4,048,910 2,024,455 6,073,366 3,036,683 9,110,050 4,555,025 13,665,076 6,832,538 3,416,269 10,248,808 5,124,404 2,562,202 1,281,101 3,843,304 1,921,652 960,826 480,413 1,441,240 720,620 360,310 180,155 540,466 270,233 810,700 405,350 202,675 608,026 304,013 912,040 456,020 228,010 114,005 342,016 171,008 85,504 42,752 21,376 10,688 5,344 2,672 1,336 668 334 167 502 251 754 377

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