Base Divisibility

Explore divisors, terminating fractions, and rhet arithmetic for any base

Enter a Base

360 = 2 × 2 × 2 × 3 × 3 × 5

Divisors of Base 360

24 divisors

1234568910121518202430364045607290120180360

Terminating Fractions in Base 360

1/n terminates when every prime factor of n is also a prime factor of the base

1/2✓ Terminates

0;180

1/3✓ Terminates

0;120

1/4✓ Terminates

0;90

1/5✓ Terminates

0;72

1/6✓ Terminates

0;60

1/7✗ Repeats

1/8✓ Terminates

0;45

1/9✓ Terminates

0;40

1/10✓ Terminates

0;36

1/12✓ Terminates

0;30

1/15✓ Terminates

0;24

1/16✓ Terminates

0;22 180

1/20✓ Terminates

0;18

1/24✓ Terminates

0;15

1/30✓ Terminates

0;12

1/36✓ Terminates

0;10

1/60✓ Terminates

0;6

1/120✓ Terminates

0;3

1/180✓ Terminates

0;2

1/360✓ Terminates

0;1

Decimal → Rhet (Base 360)

Multiply the decimal by the base. The whole number is your first rhet digit. Take what's left over and multiply by the base again. Repeat until nothing remains.

#10.375×360=135→digit 135remainder: 0

Result: 0;135

Rhet → Decimal (Base 360)

Take each rhet digit and divide by the base — once for the first digit, twice (base × base) for the second, three times (base × base × base) for the third. Add them all up.

#150÷360=0.1388888889

#2350÷360 × 360=0.002700617284

Sum = 0.1415895062

Multiplying Two Rhet Numbers (Base 360)

Multiply each pair of digits. Divide by the base once for each rhet position involved (first digit × first digit = divide twice, etc.). Add all the pieces, then convert back to rhet.

50×120=6000÷360 × 360

Decimal product = 0.046296296296296294

Rhet product = 0;16 240