7,506,640

2⁴ × 5 × 103 × 911

Starting at 7,506,640, the Collatz iteration reaches 1 after 111 steps. The first transition is 3753320; the starting value is even with 40 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 5 × 103 × 911

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 40

Divisor Sum (σ) 17,641,728

Proper Divisor Sum 10,135,088

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #7506637 ← → #7506647

Radix Representation

Decimal	7506640
Binary	11100101000101011010000 (23 bits)
Octal	0o34505320
Hexadecimal	0x728AD0

Divisor Catalog (40)

1 2 4 5 8 10 16 20 40 80 103 206 412 515 824 911 1,030 1,648 1,822 2,060 3,644 4,120 4,555 7,288 8,240 9,110 14,576 18,220 36,440 72,880 93,833 187,666 375,332 469,165 750,664 938,330 1,501,328 1,876,660 3,753,320 7,506,640

Collatz Trajectory (111 steps to reach 1)

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

7,506,640 3,753,320 1,876,660 938,330 469,165 1,407,496 703,748 351,874 175,937 527,812 263,906 131,953 395,860 197,930 98,965 296,896 148,448 74,224 37,112 18,556 9,278 4,639 13,918 6,959 20,878 10,439 31,318 15,659 46,978 23,489 70,468 35,234 17,617 52,852 26,426 13,213 39,640 19,820 9,910 4,955 14,866 7,433 22,300 11,150 5,575 16,726 8,363 25,090 12,545 37,636 18,818 9,409 28,228 14,114 7,057 21,172 10,586 5,293 15,880 7,940

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