Remainder Tests 2 - 10

Remainder Tests from 2 - 10
2 - Take the right most digit of a very big number and take its modulus by 2. You can ignore the rest of the digts. The remainder will be the same as the remainder when the whole number divides by 2.
Example: What is the remainder when 1036125837 is divided by 2?
The last digit of the number is 7.
7 modulus 2 = 1.
Remainder = 1

3 - Take the sum of all the digits of a very big number. Next, after finding the sum, take its modulus by 3. The remainder will be the same as finding the remainder when the whole number divides by 3.
Example: What is the remainder when 1036125837 is divided by 3?
Sum = 1 + 0 + 3 + 6 + 1 + 2 + 5 + 8 + 3 + 7 = 36
36 modulus 3 = 0.
Remainder = 0

4 - (1, 2) No period.
The sequence that is shown on the left is only applied on the two right most digits only. Multiply the right most digit by 1 and multiply the second right most digit by 2. Add both of them together and take the modulus of 4.
Example: What is the remainder when 1036125837 is divided by 4?
The last two digits of the number is 37.
Multiplication of the right most digit: 7 x 1 = 7
Multiplication of the left most digit: 3 x 2 = 6
Sum = 7 + 6 = 13
13 modulus 4 = 1, Remainder = 1

5 - Take the right most digit and take its modulus of 5.
Example: What is the remainder when 1036125837 is divided by 5?
Rightmost digit = 7
7 modulus 5 = 2, Remainder = 2

6 - (1, -2, -2, -2, -2, and -2 goes on for the rest)No period
Minimum magnitude sequence
(1, 4, 4, 4, 4, and 4 goes on for the rest)
Positive sequence
Multiply the right most digit by the left most digit in the sequence and multiply the second right most digit by the second left most digit in the sequence and so on. Next, compute the sum of all the values and take the modulus of 6.
Example: What is the remainder when 1036125837 is divided by 6?
Multiplication of the rightmost digit = 1 x 7 = 7
Multiplication of the second rightmost digit = 3 x -2 = -6
Third rightmost digit = -16, Fourth rightmost digit = -10,
Fifth rightmost digit = -4, Sixth rightmost digit = -2
Seventh rightmost digit = -12, Eighth rightmost digit = -6
Ninth rightmost digit = 0, Tenth rightmost digit = -2
Sum = -51
-51 modulus 6 = 3
Remainder = 3

7 - (1, 3, 2, -1, -3, -2, cycle repeats for the next six digits) Period: 6 digits.
Recurring numbers: 1, 3, 2, -1, -3, -2
Minimum magnitude sequence
(1, 3, 2, 6, 4, 5, cycle repeats for the next six digits) Period: 6 digits.
Recurring numbers: 1, 3, 2, 6, 4, 5
Positive sequence
Multiply the right most digit by the left most digit in the sequence and multiply the second right most digit by the second left most digit in the sequence and so on and so for. Next, compute the sum of all the values and take the modulus of 7.
Example: What is the remainder when 1036125837 is divided by 7?
Multiplication of the rightmost digit = 1 x 7 = 7
Multiplication of the second rightmost digit = 3 x 3 = 9
Third rightmost digit = 8 x 2 = 16, Fourth rightmost digit = 5 x -1 = -5,
Fifth rightmost digit = 2 x -3 = -6, Sixth rightmost digit = 1 x -2 = -2
Seventh rightmost digit = 6 x 1 = 6, Eighth rightmost digit = 3 x 3 = 9
Ninth rightmost digit = 0, Tenth rightmost digit = 1 x -1 = -1
Sum = 33
33 modulus 7 = 5
Remainder = 5


8 - (1, 2, 4) No period.
The sequence shown on the left is only appliable on the three extreme right digits of a very big number. The rest of the digits can be ignored.
Multiply the right most digit by 1 and multiply the second right most digit by 2 and multiply the third rightmost digit by 4. Add all of them together and take the modulus of 8.
Example: What is the remainder when 1036125837 is divided by 8?
Multiplication of the rightmost digit = 7 x 1 = 7
Multiplication of the second rightmost digit = 3 x 2 = 6
Multiplication of the third rightmost digit = 8 x 4 = 32
Sum = 45
45 modulus 8 = 5
Remainder = 5


9 - It is similar to the remainder test of 3. Take the sum of all the digits of a very big number. Next, after finding the sum, take its modulus by 9. The remainder will be the same as finding the remainder when the whole number divides by 9.
Example: What is the remainder when 1036125837 is divided by 9?
Sum = 1 + 0 + 3 + 6 + 1 + 2 + 5 + 8 + 3 + 7 = 36
36 modulus 9 = 0.
Remainder = 0

10 - Take the rightmost digit of a very large number. The remainder is simply that digit itself. lol.
Example: What is the remainder when 1036125837 is divided by 10?
Rightmost digit = 7
Remainder = 7

This ends this post from 2 - 10.