Table of congruences
A table of congruences is like a chart that helps us figure out if two numbers have something in common. When we say two numbers are congruent, it means they have the same remainder when divided by a certain number.
For example, let's say we want to know if 8 and 17 are congruent when we divide by 3. We can use the table of congruences to help us figure it out.
We start by writing down the numbers we want to check, in this case 8 and 17. Then we write down the number we want to divide by, which is 3.
Next, we write down all the possible remainders when we divide by 3. These are 0, 1, and 2.
Under each remainder, we write down all the numbers that leave that remainder when divided by 3. For example, 0 is the remainder we get when we divide 6 or 9 by 3. So we write down 6 and 9 under the 0 column.
Now we look at the numbers we want to check, 8 and 17. We divide each of them by 3 and see what remainder we get.
8 divided by 3 is 2, so we look under the 2 column and see that the numbers that leave a remainder of 2 when divided by 3 are 2, 5, 8, 11, 14, 17. 8 is one of these numbers, so it is congruent to 17 when we divide by 3.
So, in the end, we know that 8 and 17 are congruent when we divide by 3.
Overall, the table of congruences is a helpful tool for figuring out if numbers have something in common when we divide them by a certain number.
For example, let's say we want to know if 8 and 17 are congruent when we divide by 3. We can use the table of congruences to help us figure it out.
We start by writing down the numbers we want to check, in this case 8 and 17. Then we write down the number we want to divide by, which is 3.
Next, we write down all the possible remainders when we divide by 3. These are 0, 1, and 2.
Under each remainder, we write down all the numbers that leave that remainder when divided by 3. For example, 0 is the remainder we get when we divide 6 or 9 by 3. So we write down 6 and 9 under the 0 column.
Now we look at the numbers we want to check, 8 and 17. We divide each of them by 3 and see what remainder we get.
8 divided by 3 is 2, so we look under the 2 column and see that the numbers that leave a remainder of 2 when divided by 3 are 2, 5, 8, 11, 14, 17. 8 is one of these numbers, so it is congruent to 17 when we divide by 3.
So, in the end, we know that 8 and 17 are congruent when we divide by 3.
Overall, the table of congruences is a helpful tool for figuring out if numbers have something in common when we divide them by a certain number.