126,180

2² × 3² × 5 × 701

126,180 has digital root 9. The neighboring primes are 126173 and 126199; its proper-divisor sum differs from the starting integer by 130,932.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 5 × 701

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 383,292

Proper Divisor Sum 257,112

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #126173 ← → #126199

Radix Representation

Decimal	126180
Binary	11110110011100100 (17 bits)
Octal	0o366344
Hexadecimal	0x1ECE4

Divisor Catalog (36)

1 2 3 4 5 6 9 10 12 15 18 20 30 36 45 60 90 180 701 1,402 2,103 2,804 3,505 4,206 6,309 7,010 8,412 10,515 12,618 14,020 21,030 25,236 31,545 42,060 63,090 126,180

Collatz Trajectory (87 steps to reach 1)

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

126,180 63,090 31,545 94,636 47,318 23,659 70,978 35,489 106,468 53,234 26,617 79,852 39,926 19,963 59,890 29,945 89,836 44,918 22,459 67,378 33,689 101,068 50,534 25,267 75,802 37,901 113,704 56,852 28,426 14,213 42,640 21,320 10,660 5,330 2,665 7,996 3,998 1,999 5,998 2,999 8,998 4,499 13,498 6,749 20,248 10,124 5,062 2,531 7,594 3,797 11,392 5,696 2,848 1,424 712 356 178 89 268 134

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