# How to find and check the factors of a number

March 23, 2014 *by:*
** Abhijit Bangal** Points: 12 Category:

**Maths**
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Here is a simple guide on how you can find and check the factors of a number.

Finding the factors of a number is a common part of the syllabus for many students. If the students aren't well-prepared to carry this out, it all looks very tedious and difficult. Actually, finding the factors of a number is a very interesting thing, provided there are some basic things that the students should make themselves well-known with.

In this short example, I will be showing how you can find the factors of 72 and check them all. It includes checking for duplicate factors or for those you missed if any. Now, why I chose to calculate factors of 72 is because, 72 is one such number that can be divided by both an even number 2, and an odd number 3.

It's not like other numbers can't be divided by an even and an odd number at the same time, it's the matter of just feeling comfortable with 72.

But before starting, you must remember a thumb rule that no factor of any number is ever great than half of that number. So, in case of 72, all the divisors will be equal to or less than 36.

So, here's how we begin. Every number is divisible by 1 and so is 72. So, 1 is the first factor of 72. As per the test of divisibility by 2, any number having 0, 2, 4, 6 or 8 in the unit's place is divisible by 2. So, 72 is also divisible by 2. That's why the second factor of 72 is 2.

72 is also divisible by 3, because, the sum of 72 is 7 + 2 = 9.

72 can be divided by 4, as 4 is in the table of 2. And this can also be seconded by the test of divisibility by 4. 72 is divisible by 6, because according to the test of divisibility by 6, those numbers can be divided by 6 that are divisible by 2 and 3.

8 is in the table of 4 (which can also divide 72). That's why 72 can be divided by 8 as well. The sum of the digits of 72 is 9. So, 72 is also divisible by 9.

So, until now, the divisors that we have found are 1, 2, 3, 4, 6, 8 and 9. Now, this is a very interesting point where we have reached. Mark the last two digits - 8 and 9. These are two consecutive natural numbers that are the factors of 72. This doesn't happen always. But keep a watch to find out if it does while finding the factors.

Finding the rest of the divisors is very easy in such a scenario.

72 = 8 X 9. Like this you can pair each factor to find the remaining divisors. Using this method, you neither miss out on any factor nor do you repeat any. The remaining pairs to complete are for the divisors 6, 4, 3, 2 and 1 - in the reverse order. So, what number will pair up with 6? The answer is 72/6 =? 72/6 = 12. So, the next divisor that will come after 9 is 12. You need not spend time confirming if 10 and 12 are the divisors of 72 or not.

Next, you have to pair 4 with the next divisor. 72/4 = 18. The pair of 3 will be with 24, because, 72/3 = 24. In that order, the next divisor will be 36 - the half of 72. The last divisor will be 72 - the number itself.

72 = 8 X 9; 72 = 6 X 12; 72 = 4 X 18; 72 = 3 X 24; 72 = 2 X 36; 72 = 1 X 72.

So, that is how you can check the factors of 72. And here's the list:

72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

I hope I have made things easier through this explanation.