7,632,138

2 × 3 × 31 × 37 × 1109

Starting at 7,632,138, the Collatz iteration reaches 1 after 173 steps. The first transition is 3816069; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2 × 3 × 31 × 37 × 1109

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 16,197,120

Proper Divisor Sum 8,564,982

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #7632089 ← → #7632143

Radix Representation

Decimal	7632138
Binary	11101000111010100001010 (23 bits)
Octal	0o35072412
Hexadecimal	0x74750A

Divisor Catalog (32)

1 2 3 6 31 37 62 74 93 111 186 222 1,109 1,147 2,218 2,294 3,327 3,441 6,654 6,882 34,379 41,033 68,758 82,066 103,137 123,099 206,274 246,198 1,272,023 2,544,046 3,816,069 7,632,138

Collatz Trajectory (173 steps to reach 1)

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

7,632,138 3,816,069 11,448,208 5,724,104 2,862,052 1,431,026 715,513 2,146,540 1,073,270 536,635 1,609,906 804,953 2,414,860 1,207,430 603,715 1,811,146 905,573 2,716,720 1,358,360 679,180 339,590 169,795 509,386 254,693 764,080 382,040 191,020 95,510 47,755 143,266 71,633 214,900 107,450 53,725 161,176 80,588 40,294 20,147 60,442 30,221 90,664 45,332 22,666 11,333 34,000 17,000 8,500 4,250 2,125 6,376 3,188 1,594 797 2,392 1,196 598 299 898 449 1,348

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