76,180

2² × 5 × 13 × 293

Starting at 76,180, the Collatz iteration reaches 1 after 37 steps. The first transition is 38090; the starting value is even with 24 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 5 × 13 × 293

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 172,872

Proper Divisor Sum 96,692

Digit Sum / Digital Root 22 (Root: 4)

Adjacent Primes #76163 ← → #76207

Radix Representation

Decimal	76180
Binary	10010100110010100 (17 bits)
Octal	0o224624
Hexadecimal	0x12994

Divisor Catalog (24)

1 2 4 5 10 13 20 26 52 65 130 260 293 586 1,172 1,465 2,930 3,809 5,860 7,618 15,236 19,045 38,090 76,180

Collatz Trajectory (37 steps to reach 1)

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

76,180 38,090 19,045 57,136 28,568 14,284 7,142 3,571 10,714 5,357 16,072 8,036 4,018 2,009 6,028 3,014 1,507 4,522 2,261 6,784 3,392 1,696 848 424 212 106 53 160 80 40 20 10 5 16 8 4 2 1

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