17 leaves a remainder of 5 when divided by 12 (12*1 + 5 = 17).

If the number is 8k + 5, then when divided by 4, the remainder is 1 (5 % 4 = 1).

13 leaves a remainder of 5 when divided by 8 (8*1 + 5 = 13).

The number can be expressed as 10k + 7. When divided by 5, the remainder is 7 mod 5, which is 2.

The sum of the remainders is 4 + 4 = 8, and 8 divided by 7 gives a remainder of 1.

Both numbers can be expressed as 6k + 4. Their sum is 12k + 8, which gives a remainder of 2 when divided by 6.

The remainder when 123 is divided by 10 is 3, as 123 = 10*12 + 3.

When 37 is divided by 5, it goes 7 times (7*5=35) with a remainder of 2 (37-35=2).

1000 divided by 6 gives a quotient of 166 and a remainder of 4.

1000 divided by 9 gives a remainder of 1 (1000 = 9*111 + 1).

The remainder when a number is divided by 10 is the last digit of the number, which is 6.

123456 mod 11 = 0, as 123456 is divisible by 11.

144 divided by 11 gives a remainder of 1.

145 divided by 12 gives a remainder of 1.

250 divided by 7 gives a quotient of 35 and a remainder of 5.

256 divided by 11 gives a quotient of 23 and a remainder of 3.

256 divided by 7 gives a quotient of 36 and a remainder of 4.

256 divided by 9 gives a quotient of 28 and a remainder of 4.

The sum of the digits of 987654 is 39, which is divisible by 9, hence the remainder is 0.

The remainder when a number is divided by 9 can be found by summing its digits. The sum of the digits of 987654321 is 45, which is divisible by 9, hence the remainder is 0.

100 divided by 6 gives a quotient of 16 and a remainder of 4.

100 divided by 8 gives 12 with a remainder of 4 (100 - 96 = 4).

1000 divided by 6 gives a remainder of 4.

1000 divided by 9 gives a remainder of 1.

1001 divided by 7 gives 143 with a remainder of 2 (1001 - 7*143 = 2).

256 divided by 11 gives a quotient of 23 and a remainder of 3 (256 - 23*11 = 3).

256 divided by 15 gives a quotient of 17 and a remainder of 1 (256 - 255 = 1).

45 divided by 8 gives a quotient of 5 and a remainder of 5.

The divisor must be greater than the remainder, so 15 is a valid divisor (45 = 15*3 + 0).

The divisor must be greater than the remainder, so 6 is a valid divisor (56 = 6*9 + 2).