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When we talk about remainders, we are talking about the amount left over after a division. For example, if we divide 10 by 3, we get a quotient of 3 and a remainder of 1. In this case, the quotient is the number of times the divisor goes into the dividend evenly, and the remainder is the amount left over.
So what happens when a number is divisible by 42 and gives a remainder of 25? Well, let’s first look at what it means for a number to be divisible by another number. A number is divisible by another number if it can be divided evenly without leaving a remainder. For example, 10 is divisible by 2 because 2 goes into 10 evenly with no remainder.
Now let’s look at the problem at hand. We know that when a number is divisible by 42 it gives a remainder of 25. This means that any number that is divisible by 42 can be written as:
“`
42n + 25
“`
where `n` is an integer. For example, if `n` is 1, then the number is `42(1) + 25 = 67`. If `n` is 2, then the number is `42(2) + 25 = 109`.
Now we want to know what happens when a number that is divisible by 42 is also divisible by 14. In other words, we want to find the remainder when a number of the form `42n + 25` is divided by 14.
To do this, we need to find an equivalent expression for `42n + 25` that has a smaller coefficient for `n`. We can do this by factoring out `14` from both `42` and `25`, like so:
“`
42n + 25 = (14 * 3)n + (14 * 1) + 11
= (14 * (3n + 1)) + 11
“`
So now we have an equivalent expression for `42n + 25` that has a smaller coefficient for `n`. We can use this expression to find the remainder when a number of the form `42n + 25` is divided by `14`.
“`
(14 * (3n + 1)) + 11 = (14 * (3n + 1)) + (14 – 3)
= (14 * (3n + 1)) – (14 * (-1)) + (-3)
= (14 * (3n + 2)) – 3
“`
So the remainder when a number of the form `42n + 25` is divided by `14` is `(-3)`, which is equivalent to `11`. Therefore, if a number is divisible by `42` and also divisible by `14`, then it gives a remainder of `11`.
Here are some websites that discuss When A Number Is Divisible By 42 It Gives The Remainder 25 What Will Be The Remainder If The Number Is Divisible By 14:
– [math.stackexchange.com](https://math.stackexchange.com/questions/417977/when-a-number-is-divisible-by-42-it-gives-the-remainder-25-what-will-be-the
