Question

What are the factors of 72?

Answer 1

Hint: For the given question, first let’s look at the definition of the factors of a number. A factor is a number that divides a number and given no or zero remainder. For example, if we divide 6 by 2 we get the quotient 3 and remainder 0, so 2 is a factor of 6. Similarly, if we divide 6 by 3 we get remainder 0 hence 3 is also a factor of 6. We can easily state that 1 is a common factor to all numbers, also any number is a factor of itself.

Complete step by step solution:
We are asked to find the factors of 72, to do this we will first find the factors of 72 that lie from 1 to 9.
As we already know that 1 is a factor of all numbers, we do not have to consider it. By dividing 72 by 2, we get remainder 0, so 2 is a factor of 72. Similarly, when we divide 72 by 3 we get remainder 0, so 3 is also a factor. By following this same method for all integers till 9, we get the factors from 1 to 9 as: 1, 2, 3, 4, 6, 8, and 9.
Now to find the other factors that are larger than 9, we will divide 72 with the factors we got in above step. The quotient of the division will be the remaining factors.
We can easily divide 72 by 2, 3, 4, 6, 8, and 9 and get the quotient as 36, 24, 18, 12, 9, 8 respectively. These are the remaining factors. Writing all the factors we got so far along with 1 and 72, we get total factors as 1, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

Note: The reasoning behind the above method is that the factors that are greater than 9 are will be the quotient in division, any factor of 72 greater than 9 must be multiplied by something less than 8 to get 72.