# A number when divided by 28, leaves a remainder of 7. How do you find the remainder when the same number is divided by 35?

##### 1 Answer

Sometimes, in attempting to answer a question about numbers, it is helpful to look at some examples.

#### Explanation:

Below are the first 11 (positive) numbers that leave a remainder of

Look at the first three columns:

First of all, it is now clear that knowing only the remainder when a number is divided by

But there is a pattern. So we don't need complete information about the original number or about

The pattern has a cycle of 5 values, so it makes sense to look at the fourth column, the remainder when

Writing the result and proving it for all possible