Question

Write the next whole number after 6467 in the base-eight system.

Answer 1

30541

Explanation:

8⁰ = 1

8¹ = 8

8² = 64

8³ = 512

8⁴ = 4096

8⁵ = 32768 > 6467

We have

6467 ÷ 8⁴ = 1 (mod 2371)

2371 ÷ 8³ = 4 (mod 323)

323 ÷ 8² = 5 (mod 3)

3 ÷ 8 = 0 (mod 3)

3 ÷ 1 = 3

=> 6467 in the base-eight system: 30541