Find the least positive integer which gives remainder 1 when divided by 13, and remainder 2 when divided by 31.

The required integer is 157.

Step-by-step explanation:

Let the unknown number be x.

It is given that the remainder 1 when x is divided by 13, and remainder 2 when x is divided by 31.

Here,

13 and 31 hare prime numbers. so the GCD o 13 and 31 is

Using Chinese remainder theorem, we get

The formula to find the value of x is

Substitute the given values in the above formula.

Let n=-1, because we need to find the least positive integer.

Therefore, the required integer is 157.

150.6

all i did was i multiplied 5.02 by 30

0.0076, if you meant 4.125 divided by 0.03125 it would be 132

step-by-step explanation:

first you have to move the decimal in 0.03125 over until its behind the 5 which is 5 places over. now the number is 3125

then you have to move the decimal in 4.125, 5 places over. now the number is 4,112,500.

now you divide like you would normally would and get 0.0076