7,427,584

2⁹ × 89 × 163

For 7,427,584, the 40 positive divisors have a total of 15,099,480. Removing 7,427,584 leaves 7,671,896, which gives the abundant classification.

Prime Factor Structure

Factorization String 2^9 × 89 × 163

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 40

Divisor Sum (σ) 15,099,480

Proper Divisor Sum 7,671,896

Digit Sum / Digital Root 37 (Root: 1)

Adjacent Primes #7427573 ← → #7427591

Radix Representation

Decimal	7427584
Binary	11100010101011000000000 (23 bits)
Octal	0o34253000
Hexadecimal	0x715600

Divisor Catalog (40)

1 2 4 8 16 32 64 89 128 163 178 256 326 356 512 652 712 1,304 1,424 2,608 2,848 5,216 5,696 10,432 11,392 14,507 20,864 22,784 29,014 41,728 45,568 58,028 83,456 116,056 232,112 464,224 928,448 1,856,896 3,713,792 7,427,584

Collatz Trajectory (80 steps to reach 1)

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

7,427,584 3,713,792 1,856,896 928,448 464,224 232,112 116,056 58,028 29,014 14,507 43,522 21,761 65,284 32,642 16,321 48,964 24,482 12,241 36,724 18,362 9,181 27,544 13,772 6,886 3,443 10,330 5,165 15,496 7,748 3,874 1,937 5,812 2,906 1,453 4,360 2,180 1,090 545 1,636 818 409 1,228 614 307 922 461 1,384 692 346 173 520 260 130 65 196 98 49 148 74 37

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