Thursday

July 24, 2014

July 24, 2014

Posted by **jamie** on Thursday, June 7, 2007 at 12:51pm.

remainder of 3 when divided by 4 and a remainder of 4 when divided by 5?

The answer is 59. There is a general method for solving such problms, but in this case you can use this trick. First, note that you don't have to demand that the remainder is 1 when divided by 2 becuse that follows from the fact that the remainder is 3 when divided by 4.

The number 60 is the product of 3, 4, and 5. All the remainders for 60 are thus zero and 60 is the smallest positive number with this property. Now, all the remainders of 60 + x are equal to x. But if x is equal or larger than y then the remainder after division by y is obtained by subtracting y until the number becomes less than y. In case x is negative you have to add y as many times to make the number equal or larger to zero.

If we take x equal to -1, then all the remainders are -1 plus the number you are dividing with, so it's one less than the number, which is exactly what we want.

**Related Questions**

Math - How many integers between 200 and 500 inclusive leave a remainder 1 when ...

Math - How many integers bewteen 200 and 500 inclusive leave a remainder 1 when ...

Math - Find the least positive integer that leaves the remainder 3 when divided...

Math - repost for Anonymous - Can someone show me the steps to these questions (...

math - what is the least common positive integer that meets the following ...

math - what is the least common positive integer that meets the following ...

math - When a is divided by 7,the remainder is 4.When b is divided by 3,the ...

Math - Find the smallest positive integer that leaves a remainder of 5 when ...

number theory - Find the least positive integer that leaves the remainder 3 ...

math proportions - The remainder is a fraction (remainder/divisor). Why dont you...