What are all of the factors of 45? If you want the easy answer, I’ll give it to you: 1, 3, 5, 9, 15, and 45.

However, if you want to learn how I came up with these answers and discover an easy method to learn all the factors of 45 (or any whole number) yourself, keep reading.

What is factoring?

Factoring is a math skill you’ll need to know to do well on the SAT or ACT. Simply put, factoring is the technique used to determine factors or all of the whole numbers that can divide a target number without leaving any remainder.

For example, 9 is a factor of 45 because if you divide 45 by 9, you get the whole number 5. However, 4 is not a factor of 45 because 45 divided by 4 is 11.25, which is not a whole number.

Factoring will help you find factor pairs, which are numbers you can multiply by one another to reach your target number.

For instance, 3 and 15 are factor pairs for 45 because 3*15=45.

Being able to find factors and factor pairs might not seem important now, but it will be essential for doing well on the SAT or ACT and succeeding in higher level math classes like calculus.

Factoring tips

While you can go through the tedious process of dividing your target number by every single number that has a lower value, this is not an effective way to find factors.

Here are some factoring tips to help you find factors with ease:

Use square roots and factor pairs to save time

Since factors have pairs, you can significantly reduce the amount of time it takes to find factors by calculating factor pairs, first. 

You can do this by taking the square root of your target number.

This way, you only have to see if the whole numbers that are lower than the square root are factors.

For instance, the square root of 81 is 9. This means that you only have to see if 1, 2, 3, 4, 5, 6, 7, 8, and 9 are factors because they will make up the first half of a factor pair.

For this example, 81 is evenly divisible by 1, 3, and 9.

The next step you need to take is to see what the pairs are for each of these factors. 

In this case, 81/1= 81, 81/3=27, and 81/9=9. The factor pairs here are (1,81), (3,37), and (9,81).

Altogether, this means that the factors for 81 are 1, 3, 9, 27, and 81.

You can use these steps to figure out the factors for any number. If the square root of a target number is not a whole number, simply round down to the nearest whole number.

Include “1” and the target number

Every number is evenly divisible by 1. This means that you automatically know that the number 1 and your target number are factors before you even start to do any mathematical calculations.

Before you even start to consider other possible factors, write down the number 1 and the target word.

Consider whether your target number is even or odd

If your target number is even, then it must be evenly divisible by 2. This means that you can include 2 and its factor pair when you are factoring.

If your target number is odd, then it cannot be evenly divided by 2. This means that you will already know that 2 is not a factor for an odd target number.

Pay attention to your target number ending

If your target number ends with a 0 or a 5, it can be evenly divided by 5. If your target number ends with 2, it can be evenly divided by 2. If your target number ends with 0, it will be evenly divisible by 10.

For example, without doing any calculations, I know that the target number 60 must include 0, 5, and 10 as factors no matter what.

Pay attention to repeated digits

If your target number is “44” or “66” or “99” or any other repeating double digit, it will be evenly divisible by 11.

With these tips in mind, you will be able to find all of the factors of a target number without spending too much time or energy trying to calculate these factors.

Finding the factors of 45

Now that you know a few tips and tricks for factoring, you will better understand how to find factors when you take the SAT or ACT or a math class.

We can use these tips to figure out the factors of 45 without any headache.

First, we know that both 1 and 45 are factors because the target number and the number 1 are always factors.

Second, because 45 ends with 5, we know that 5 will be a factor and 2 will not be a factor. By dividing 45 by 5, we can get its factor pair, which is 9.

Third, if we take the square root of 45, we get roughly 6.7. If we round down to the nearest whole number, we know that 6 is the largest potential first half of a factor pair. Because 45 is an odd number, then 4 and 6 cannot be factors. This means we only have to test 3. If we divide 45 by 3, we get 15, giving us two pairs (3 and 15).

That leaves us with the following factors: 1, 3, 5, 9, 15, 45.

While you can always commit these factors to memory through rote memorization, you will have an easier time with other target numbers if you memorize the tips above instead.

Other math tips

There are many skills you will need in addition to factoring to do well on the SAT or ACT. You can learn strategies to help you figure out all of the math skills you’ll need on these tests when you take an SAT or ACT prep course or work with a private math, SAT, or ACT tutor.

Prep Expert offers prep courses for standardized tests like the SAT or ACT. By taking these prep courses, you will learn more tips and tricks that will help you master the math section of these tests.

Prep Expert also offers math tutoring so that you can successfully learn math concepts, like factoring, that will help you earn a good grade in your math classes. With individualized instruction tailored to your specific needs, you will not have to worry about struggling with new math concepts covered in your classes.

Sign up for one of our prep courses or get matched with one of private tutors when you visit our website.