What is the lowest numberthat has a remainder of 1 when divided by 2 and a remainder of 2 when devided by 3 and a
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.
To solve this problem, we need to find the lowest number that satisfies the given conditions. One approach is to systematically check numbers starting from a certain point until we find one that meets all the remainders.
In this case, we can start by considering the remainder when dividing by 4. We know that the number must have a remainder of 3 when divided by 4. So, we can start by adding 3 to any number that is divisible by 4.
Let's test this approach by starting with 4. If we add 3 to 4, we get 7, which has a remainder of 2 when divided by 3. This doesn't satisfy the second condition.
Let's try adding 3 to the next multiple of 4, which is 8. If we add 3 to 8, we get 11. However, 11 does not satisfy any of the given conditions.
We can continue this process until we find a number that satisfies all the given conditions.
Now, let's consider the remainder when dividing by 5. We need a number that has a remainder of 4 when divided by 5. Instead of starting from 0, let's start from 5 and add 4 to it.
Starting from 5, if we add 4, we get 9. However, 9 does not satisfy any of the given conditions.
We can continue this process until we find a number that satisfies all the given conditions.
Finally, let's consider the remainder when dividing by 2. We need a number that has a remainder of 1 when divided by 2. Instead of starting from 0, let's start from 2 and add 2 to it.
Starting from 2, if we add 2, we get 4. However, 4 does not satisfy any of the given conditions.
We can continue this process until we find a number that satisfies all the given conditions.
After testing several numbers, we find that the number 59 satisfies all the given conditions. When divided by 2, it has a remainder of 1. When divided by 3, it has a remainder of 2. When divided by 4, it has a remainder of 3. And when divided by 5, it has a remainder of 4.
Therefore, the lowest number that satisfies all the given conditions is 59.
To find the lowest number with the given remainders, we can start with 60 and add multiples of the product of the divisors until we find a number that satisfies all the conditions.
First, let's divide 60 by 2. The quotient is 30 with a remainder of 0, which is not equal to 1. Therefore, we add the product of the divisors (2 * 3 * 4 * 5) to 60.
60 + (2 * 3 * 4 * 5) = 60 + 120 = 180
Now, let's divide 180 by 2. The quotient is 90 with a remainder of 0, which is still not equal to 1. Again, we add the product of the divisors to 180.
180 + (2 * 3 * 4 * 5) = 180 + 120 = 300
We continue this process until we find a number that satisfies all the conditions.
300 + (2 * 3 * 4 * 5) = 420
420 + (2 * 3 * 4 * 5) = 540
540 + (2 * 3 * 4 * 5) = 660
660 + (2 * 3 * 4 * 5) = 780
780 + (2 * 3 * 4 * 5) = 900
Finally, we reach a number where the remainder when divided by 2 is 1.
900 + (2 * 3 * 4 * 5) = 1020
Therefore, the lowest number that has a remainder of 1 when divided by 2, a remainder of 2 when divided by 3, a remainder of 3 when divided by 4, and a remainder of 4 when divided by 5 is 1020.