The factors of a number are the numbers that divide evenly into it, leaving no remainder. To find the factors of 65, we can start by dividing 65 by the smallest possible factor, which is 1. Since 65 divided by 1 equals 65, we know that 1 is a factor of 65.
Next, we can try dividing 65 by 2. However, 65 is an odd number, so it is not divisible by 2. We can continue testing for factors by dividing 65 by 3, 4, 5, and so on.
Dividing 65 by 3 gives us 21 with a remainder of 2, so 3 is not a factor of 65. Dividing 65 by 4 gives us 16 with a remainder of 1, so 4 is not a factor of 65 either.
However, dividing 65 by 5 gives us 13 with no remainder, so 5 is a factor of 65. We can also find that 13, the result of dividing 65 by 5, is a factor of 65 by checking whether dividing 65 by 13 results in an integer. Indeed, 65 divided by 13 equals 5 with no remainder.
We can stop testing for factors once we reach the square root of 65, which is approximately 8.06. This is because any factor of 65 that is greater than the square root of 65 must pair up with a factor that is less than the square root of 65, such that their product equals 65.
Therefore, the factors of 65 are 1, 5, 13, and 65. In summary, to find the factors of 65, we test for divisibility by integers starting from 1 up to the square root of 65, and any resulting integer quotient with no remainder is a factor.