91Ó°ÊÓ

Division is one of the basic arithmetic operations, where we split a number, called the dividend, into equal parts. The number we divide by is called the divisor. For instance, in the exercise, we divide 52 (the dividend) by 14 (the divisor).

When doing division, we see if the divisor can fit into the dividend a certain number of times evenly. If it does, it results in an integer without any leftover, which we call the remainder. If it doesn't divide evenly, we get a result with decimals and a remainder.

An integer result in division means that after dividing the dividend by the divisor, the quotient (result) is a whole number without any fractional part. For example, dividing 10 by 2 gives us 5, which is an integer.

In our exercise, when dividing 52 by 14, we got 3.7142857142857144, which means the result is not an integer. This tells us that 14 does not divide 52 evenly.

We can quickly check for an integer result by looking for no digits after the decimal point in the quotient. If there are any, it tells us we do not have an integer result.

The remainder is what is left over after division when the divisor does not evenly go into the dividend. It is the portion of the dividend that is not evenly divisible by the divisor.

For example, dividing 7 by 2 gives us 3 with a remainder of 1, since 2 does not go into 7 evenly (2 * 3 = 6, and there's 1 left over).

In the exercise, when dividing 52 by 14, the non-integer result 3.7142857142857144 indicates that there is a remainder. To find the exact remainder, we could multiply the integer part (in this case, 3) by the divisor (14) and subtract that from the original dividend (52).

This gives us: \[ 52 - (14 \times 3) = 52 - 42 = 10 \] Therefore, the remainder in this division is 10. This confirms that 14 is not a factor of 52.