How to Calculate Mod 10

It's simple to calculate mod 10.

In modular arithmetic an integer, or whole number, is expressed as a number between zero and the modulus minus one. For example, if the modulus is 7, then any integer is equivalent to 0, 1, 2, 3, 4, 5 or 6. If you divide an integer by the modulus, the remainder is the integer's value relative to the modulus. For example, 8 mod 7 is 1 because that is the remainder when you divide 8 by 7. It's quite simple to determine the value of an integer relative to the modulus 10.

Things You'll Need

• Pencil and paper
• Calculator (optional)

Instructions

1. Write an integer on a piece of paper. For example, write "121" on your paper.

2. Write down the last digit (the "units" digit). If the number is 121, then write "1" on your paper.

3. Determine the number relative to the modulus 10 by writing the number from Step 2 if your original number is positive, and writing the value of 10 minus the number if the original number is negative. If the original number ends in zero, then your answer is zero in every case. For example, 121 mod 10 is 1 and -121 mod 10 = 10 -- 1 = 9.

References

• Better Explained: Fun With Modular Arithmetic

Resources

• Calculator