What are Factor Tables?

Some integer questions may require you to find the Factors of an integer. The factor table is a basic technique for finding all the factors of any integer. This technique…
by Talha Omer, M.Eng., Cornell Grad
in Math Concepts

Some integer questions may require you to find the Factors of an integer. The factor table is a basic technique for finding all the factors of any integer. This technique can also be useful for questions asking how many factors a particular integer has.

The technique goes as follows:

  1. Write the original integer on top of the table.
  2. Divide the original Integer by the smallest positive factor: 1. Write “1” in the left column, and the result of the division in the right column. (Of course, this will just be the original integer.)
  3. Divide the original integer by the next higher factor: 2. Write “2” in the left column, and the result of the division in the right column. If the original integer is not divisible by 2, skip 2 and move on to higher possible factors: 3, 4, 5, etc.
  4. Continue the process until the factors repeat themselves – stop when you’re trying to divide the original integer by a factor that’s already on the right side of the table.
  5. You’re done – the table now holds the positive factors of the original integer.

If you are interested in the negative factors, the negative version of every positive factor is also a factor.

Let’s look at an example: What are the positive factors of 60?

Begin by writing “60” at the top of the table. Now, divide 60 by 1. The result is, of course, 60. Write “1” and “60” in the topmost row of the table.

In this Article

60

Left Column Right Column
1 60
   
   
   
   
   
   

 

Next, divide 60 by the next higher possible factor: 2. The result of 60/2 is 30, so write “2” and “30” in the appropriate places in the second row.

60

Left Column Right Column
1 60
2 30
   
   
   
   
   
 

Continue dividing 60 by higher and higher factors – 3, 4, 5, 6, writing the results of the divisions in the right column. Skip 7, 8, and 9 (60 is not divisible by those). 

You can also use the divisibility rules here to quickly figure out if 60 is divisible by any of them.

When you reach 10, stop – it’s already on the table, in the right column. The resulting table looks thus: 

60

Left Column Right Column
1 60
2 30
3 20
4 15
5 12
6 10
10  
 

Hooray! The positive factors of 60 are the numbers in the table: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

All of the factors of 60, therefore, are ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, and ±60.

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