Find the simplest possible form of each of the following numbers, module 4

Question

1. 15
2. 32
3. 62

Answer 1

To find the simplest possible form of each number modulo 4, we will compute each number's remainder when divided by 4.

1. 15 mod 4:

   • When we divide 15 by 4, the quotient is 3 and the remainder is 3 (since \(15 = 4 \times 3 + 3\)).
   • Therefore, \(15 \mod 4 = 3\).

2. 32 mod 4:

   • When we divide 32 by 4, the quotient is 8 and the remainder is 0 (since \(32 = 4 \times 8 + 0\)).
   • Therefore, \(32 \mod 4 = 0\).

3. 62 mod 4:

   • When we divide 62 by 4, the quotient is 15 and the remainder is 2 (since \(62 = 4 \times 15 + 2\)).
   • Therefore, \(62 \mod 4 = 2\).

In summary, the simplest possible forms of the given numbers modulo 4 are:

1. \(15 \mod 4 = 3\)
2. \(32 \mod 4 = 0\)
3. \(62 \mod 4 = 2\)