λ
Ratio Atlas
Atlas › Integer Profiles › Node 72,097,656

72,097,656

23 × 3 × 233 × 12893
Abundant Even Composite

72,097,656 factors as 2^3 × 3 × 233 × 12893. Its 32 positive divisors give a proper-divisor sum of 108,934,104, so this integer is abundant. The Collatz stopping time is 197 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 233 × 12893
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 181,031,760
Proper Divisor Sum 108,934,104
Digit Sum / Digital Root 42 (Root: 6)
Adjacent Primes #72097633 ← → #72097667

Radix Representation

Decimal 72097656
Binary 100010011000001111101111000 (27 bits)
Octal 0o423017570
Hexadecimal 0x44C1F78

Divisor Catalog (32)

1 2 3 4 6 8 12 24 233 466 699 932 1,398 1,864 2,796 5,592 12,893 25,786 38,679 51,572 77,358 103,144 154,716 309,432 3,004,069 6,008,138 9,012,207 12,016,276 18,024,414 24,032,552 36,048,828 72,097,656

Collatz Trajectory (197 steps to reach 1)

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

72,097,656 36,048,828 18,024,414 9,012,207 27,036,622 13,518,311 40,554,934 20,277,467 60,832,402 30,416,201 91,248,604 45,624,302 22,812,151 68,436,454 34,218,227 102,654,682 51,327,341 153,982,024 76,991,012 38,495,506 19,247,753 57,743,260 28,871,630 14,435,815 43,307,446 21,653,723 64,961,170 32,480,585 97,441,756 48,720,878 24,360,439 73,081,318 36,540,659 109,621,978 54,810,989 164,432,968 82,216,484 41,108,242 20,554,121 61,662,364 30,831,182 15,415,591 46,246,774 23,123,387 69,370,162 34,685,081 104,055,244 52,027,622 26,013,811 78,041,434 39,020,717 117,062,152 58,531,076 29,265,538 14,632,769 43,898,308 21,949,154 10,974,577 32,923,732 16,461,866

More profiles

Browse other published profiles and their separate link collections.

No other profiles in this collection.

← Previous Integer #72,097,655 Browse Full Index Next Integer #72,097,657 →