Remainder tests 26 - 30

26 - (1, 10, -4, 12, -10, 4, -12, 10, -4, 12, -10, 4, -12, 10) Period: 6 digits starting from the last two digit.
Recurring numbers: 10, -4, 12, -10, 4, -12
This is a minimum magnitude sequence.
(1, 10, 22, 12, 16, 4, 14, 10, 22, 12, 16, 4, 14, 10)
This is a positive sequence.
Example: What is the remainder when 2306451879 is divided by 26?
Multiplication of the rightmost digit = 9 x 1 = 9
Multiplication of the second rightmost digit = 7 x 10 = 70
Multiplication of the third rightmost digit = 8 x -4 = -32
Multiplication of the fourth rightmost digit = 1 x 12 = 12
Fifth rightmost digit = 5 x -10 = -50
Sixth rightmost digit = 4 x 4 = 16
Seventh rightmost digit = 6 x -12 = -72
Eighth rightmost digit = 0
Ninth rightmost digit = 3 x -4 = -12
Tenth rightmost digit = 2 x 12 = 24
Sum = -35
-35 modulus 26 = 17
Remainder = 17

27 - (1, 10, -8) Period: 3 digits
starting from the last one digit.
Recurring numbers: 1, 10, -8
This is a minimum magnitude sequence.
(1, 10, 19)
This is a positive sequence.
Example: What is the remainder when 2306451879 is divided by 26?
Multiplication of the rightmost digit = 9 x 1 = 9
Multiplication of the second rightmost digit = 7 x 10 = 70
Multiplication of the third rightmost digit = 8 x -8 = -64
Multiplication of the fourth rightmost digit = 1 x 1 = 1
Fifth rightmost digit = 5 x 10 = 50
Sixth rightmost digit = 4 x -8 = -32
Seventh rightmost digit = 6 x 1 = 6
Eighth rightmost digit = 0 x 10 = 0
Ninth rightmost digit = 3 x -8 = -24
Tenth rightmost digit = 2 x 1 = 2
Sum = 18
18 modulus 27 = 18
Remainder = 18

28 - (1, 10, -12, -8, 4, 12, 8, -4, -12, -8, 4, 12, 8, -4) Period: 6 digits
starting from the last two digits.
Recurring numbers: -12, -8, 4, 12, 8, -4
This is a minimum magnitude sequence.
(1, 10, 16, 20, 4, 12, 8, 24, 16, 20, 4, 12, 8, 24)
Example: What is the remainder when 2306451879 is divided by 28?
Multiplication of the rightmost digit = 9 x 1 = 9
Multiplication of the second rightmost digit = 7 x 10 = 70
Multiplication of the third rightmost digit = 8 x -12 = -96
Multiplication of the fourth rightmost digit = 1 x -8 = -8
Fifth rightmost digit = 5 x 4 = 20
Sixth rightmost digit = 4 x 12 = 48
Seventh rightmost digit = 6 x 8 = 48
Eighth rightmost digit = 0 x -4 = 0
Ninth rightmost digit = 3 x -12 = -36
Tenth rightmost digit = 2 x -8 = -16
Sum = 39
39 modulus 28 = 11
Remainder = 11