Question

Find the possible factors of 45, 30, and 36.

Answer 1

Hint: In order to solve this problem we need to start with factoring with the smallest prime number to get all the factors. Doing this will solve your problem and will give you the right answer.


Complete step-by-step solution:
Factor means a number or algebraic expression that divides another number or expression evenly that is with no remainder or the remainder as zero.
Now in the given question, we have to find all possible factors of 45, 30, and 36.
Certain things you need to know to find the factor of any number. That is you need to know that all the numbers are the factors of 1 and the number itself, the number of factors of the number must not be greater than the number which is to be factorized.
The first number is 45.
So, the numbers which can divide 45 without leaving the remainder as natural numbers are $1, 3, 5, 9, 15, 45.$
So, there are 6 factors of 45.
The second number is 30.
So, the numbers which can divide 30 without leaving the remainder as natural numbers are $1, 2, 3, 5, 6, 10, 15, 30.$
So, there are 7 factors of $30$.
The last number is 36.
So, the numbers which can divide 36 without leaving the remainder as natural numbers are $1, 2, 3, 4, 6, 9, 12, 18, 36.$
So, there are 9 factors of $36$.

Note: In such a type of question finding the factor of a number first starts with a prime number less than that number and then divides the number with that prime number to find the other factor. The one and the only method to check whether the number is a factor of the number or not we have to divide the number and check it to find all the factors one by one sequentially and then we also need to know that the number of factors of the number must not be greater than the number which is to be factorized and any factor must not be greater than the number to be factorized. Doing this will take you to the right answers.