221 to the base 5
this is bases (7th grade)

It sounds like you want to convert 221 from base 10 to base 5.

The largest power of 5 that fits into 221 is 5³ = 125, and

221 = 125 + 96

221 = 1•5³ + 96

The largest power of 5 that fits into the remainder 96 is 5² = 25, and

96 = 75 + 21

96 = 3•25 + 21

96 = 3•5² + 21

→   221 = 1•5³ + 3•5² + 21

The largest power of 5 that fits into the remainder 21 is 5¹ = 5, and

21 = 20 + 1

21 = 4•5¹ + 1

→   221 = 1•5³ + 3•5² + 4•5¹ + 1

Finally, 1 = 5⁰, so

221 = 1•5³ + 3•5² + 4•5¹ + 1•5⁰

and

221₁₀ = 1341₅

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are