Content

• Steps
• Advice
• Warning
• What you need

Factor of a given number are numbers that, when multiplied, will have the product of the given number. Think of it another way, all numbers are the product of many factors. Learning how to factorize - or divide a number into factors - is an important mathematical skill not only applied in basic arithmetic but also in algebra, integration, and more. See Step 1 to start learning how to factor a number!

Steps

Method 1 of 2: Analyze a Basic Integer to a factor

1. 

   Write your number. To start your analysis, you need a number - any number, but for article purposes start with a simple integer. Integer are numbers that have no fractions or decimals (whole numbers include all positive integers and negative integers).
   • Please choose number 12. Write this number down on a scratch paper.

2. 

   
   
   Find two more numbers whose product is the original number you chose. Any integer can write the product of two other integers. Even a prime number can write the product of 1 and itself. Thinking of a number as a product of two factors can make you think "backwards" - you must have wondered, "which multiplication results in this number?"
   • For our example, 12 has a few factors like 12 × 1, 6 × 2, and 3 × 4 are all equal to 12. So we can say that the factors of 12 are 1, 2, 3, 4, 6, and 12. Please use factors 6 and 2 for the purposes of this article.
   • Even numbers are especially easy to analyze because all even numbers have a factor of 2. 4 = 2 × 2, 26 = 13 × 2, etc.

3. 

   
   
   Determine if the current factors can be further analyzed. Lots of numbers - especially large numbers - can be analyzed more than once. Once you've found two factors of a given number, if a factor itself has its own factors, you can also analyze this factor to smaller factors. Depending on the case, analysis may or may not be beneficial.
   • In our example, the number 12 has been decomposed into 2 × 6. Notice that 6 also has a factor of its own - 3 × 2 = 6. So we can say that 12 = 2 × (3 × 2).

4. 

   
   
   Stop analysis when all factors are prime. Primes are numbers that are only divisible by 1 and themselves. For example, 2, 3, 5, 7, 11, 13, and 17 are prime numbers. When you have analyzed some products of prime factors, further analysis is redundant. Further analyze these performance factors by itself and one has no effect, so you can stop.
   • In our example, 12 has been decomposed into 2 × (2 × 3). 2, 2, and 3 are all prime numbers. If we analyze it further, we must decompose it to (2 × 1) × ((2 × 1) (3 × 1)), which is usually no effect at all and ignored.

5. 

   Analyze negative numbers in the same way. The way of analyzing negative numbers is almost in line with the way of analyzing positive numbers. The only difference is that the product of factors must be a negative number, so the number of factors that have a negative value must be an odd number.
   • For example, let's analyze -60. Whereby:
     • -60 = -10 × 6
     • -60 = (-5 × 2) × 6
     • -60 = (-5 × 2) × (3 × 2)
     • -60 = -5 × 2 × 3 × 2. Note that as long as the number of negative factors is an odd number, the product of all factors will be negative, as if there was only one negative factor. For example, -5 × 2 × -3 × -2 also equal to -60.
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Method 2 of 2: How to Decompose Big Numbers into Factors

1. 

   Write your number above a 2-column table. Analyzing small numbers to factors is usually quite simple, but analyzing large numbers is more complicated. Most of us will have trouble parsing a 4 or 5 digit number into prime factors without using pen and paper. Fortunately, when plotting, the process becomes a lot easier. Write your number above the T-chart with two columns - you will use this to keep track of your list of factors.
   • For our example, let's choose a 4-digit number for factor analysis, that is 6.552.

2. 

   Divide your number by the smallest prime factor possible. Divide your number by the smallest (out of 1) prime factor that your number is divisible by and leaves no remainder. Write the prime factors in the left column and enter the quotient of the row in the right column.As noted above, even numbers are easier to analyze because their smallest prime factors are always 2. On the other hand, odd numbers will have a different smallest prime factor 2.
   • In our example, since 6,552 is an even number, we know that 2 is the smallest prime factor of this number. 6,552 ÷ 2 = 3,276. In the left column, we write 2, and 3.276 in the right column.

3. 

   Continue factorization in this way. Next, divide the number in the right column by its smallest prime factor, instead of using the numbers above the table. Write the selected prime factors in the left column and the new division result in the right column. Continue this process - after each repetition, the numbers in the right column get smaller.
   • Please continue to analyze. 3.276 ÷ 2 = 1.638, so we'll write a number 2 bottom left column, and write 1.638 bottom right column. 1.638 ÷ 2 = 819, so we will write 2 and 819 on the bottom of the two columns like just now.

4. 

   Analyze odd numbers by trying to divide it by small prime factors. Finding the smallest prime factor of odd numbers is more difficult than even numbers because they don't automatically have 2 as the smallest prime factors. When you get an odd number, try dividing it by a few other small primes 2 - 3, 5, 7, 11, and so on until this odd number is divisible by a prime number and zero. leave a balance. That is the smallest prime factor.
   • For our example, we get 819. 819 is an odd number, so 2 is not a factor of 819. Instead of writing 2, we will try the next prime number: 3. 819 ÷ 3 = 273 and there is no remainder, so we write 3 and 273.
   • When guessing factors, you should try all prime numbers that are less than or equal to the square root of the biggest factor you have found. If your number isn't fully divisible by any factor, you're probably trying to decompose a prime number, and the factor analysis might stop there.

5. 

   Continue until the quotient is 1. Continue dividing the number in the right column by its smallest prime until you have the number in the right column. Divide this number by itself - this will record the number in the left column and "1" in the right column.
   • Let's complete our figure analysis. See detailed explanation below:
     • Next divide by 3: 273 ÷ 3 = 91, there is no remainder, so we write 3 and 91.
     • Let's try 3: 3 is not a factor of 91, and the smallest prime number that follows (5) is also not a factor of 91, but 91 ÷ 7 = 13, there is no remainder. write 7 and 13.
     • Keep trying with 7: 7 which is not a factor of 13, 11 (the prime number immediately follows), but 13 has a factor that is itself: 13 ÷ 13 = 1. So, to complete the table. analysis, we write 13 and 1. We can stop analyzing here.

6. 

   The numbers in the left column are factors of the number you originally selected. When the right column ends with the number 1, you're done. The numbers in the left column are exactly what you are looking for. In other words, the product of those numbers will be the same as the number shown on the board. If these factors are repeated more than once, you can use the exponentiation notation to save space. For example, if your factor sequence has four 2s, you could write 2 instead of 2 × 2 × 2 × 2.
   • In our example, 6.552 = 2 × 3 × 7 × 13. This is the complete result after analyzing 6,552 as a prime factor. Regardless of the order in which the multiplication is performed, the final product will equal 6,552.
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Advice

• One important point is the concept of numbers element: a number that has only two factors of 1 and itself. 3 is prime because its factors are only 1 and 3. On the contrary, 4 has another factor of 2. A number that is not a prime number is called number combination. (The number 1 itself is not considered prime and is also not a composite - that's the case.)
• The smallest primes are 2, 3, 5, 7, 11, 13, 17, 19, and 23.
• Understand that a number is considered factor of another larger number if the greater number "is divisible by the smaller number" - that is, the larger number is divisible by the smaller number and leaves no remainder. For example, 6 is a factor of 24, because 24 ÷ 6 = 4 and there is no remainder. In contrast, 6 is not a factor of 25.
• Some numbers can be analyzed in a faster way, but the above approach is always effective, and furthermore, prime factors are listed in ascending order as you are done.
• Remember we only mention "natural numbers" - sometimes referred to as "counts": 1, 2, 3, 4, 5 ... We won't go into negative numbers or fractions, that can be addressed in separate articles.
• If the sum of the digits of the number is divisible by three, then three is a factor of the dividend. (819 has the sum of the digits 8 + 1 + 9 = 18, 1 + 8 = 9. Three is a factor of nine, so it's also a factor of 819.)

Warning

• Don't do unnecessary extra work. Once you have removed a factor value, you don't need to try again. Once we are sure that 2 is not a factor of 819, we don't need to try again with 2 for the rest of the process.

What you need

• Paper
• Writing point, use a pencil and eraser
• Computer (optional)