To begin factoring, all you need is a number - any number will do, but, for our purposes, let's start with a simple integer. Integers are numbers without fractional or decimal components (all positive and negative whole numbers are integers). Let's choose the number 12. Write this number down on a piece of scratch paper. Any integer can be written as the product of two other integers. Even prime numbers can be written as the product of 1 and the number itself. Thinking of a number as the product of two factors can require "backwards" thinking - you essentially must ask yourself, "what multiplication problem equals this number?"  In our example, 12 has multiple factors - 12 × 1, 6 × 2, and 3 × 4 all equal 12. So, we can say that 12's factors are 1, 2, 3, 4, 6, and 12. For our purposes, let's work with the factors 6 and 2. Even numbers are especially easy to factor because every even number has 2 as a factor. 4 = 2 × 2, 26 = 13 × 2, etc. Lots of numbers - especially large ones - can be factored multiple times. When you've found two of a number's factors, if one has its own set of factors, you can reduce this number to its factors as well. Depending on the situation, it may or may not be beneficial to do this. For instance, in our example, we have reduced 12 to 2 × 6. Notice that 6 has its own factors - 3 × 2 = 6. Thus, we can say that 12 =  2 × (3 × 2). Prime numbers are numbers greater than 1 that are evenly divisible only by themselves and 1. For instance, 2, 3, 5, 7, 11, 13, and 17 are all prime numbers. When you've factored a number so that it's the product of exclusively prime numbers, further factoring is superfluous. It does you no good to reduce each factor to itself times one, so you may stop. In our example, we've reduced 12 to 2 × (2 × 3). 2, 2, and 3 are all prime numbers. If we were to factor further, we'd have to factor to (2 × 1) × ((2 × 1)(3 × 1)), which isn't typically useful, so it's usually avoided. Negative numbers can be factored nearly identically to how positive numbers are factored. The sole difference is that the factors must multiply together to make a negative number as their product, so an odd number of the factors must be negative. For example, let's factor -60. See below:  -60 = -10 × 6 -60 = (-5 × 2) × 6 -60 = (-5 × 2) × (3 × 2) -60 = -5 × 2 × 3 × 2. Note that having an odd number of negative numbers besides one will give the same product. For example, -5 × 2 × -3 × -2 also equals 60.
اكتب العدد. حدد رقمين حاصل ضربهما يعطيك العدد الأول. انظر إن كان أيًا من العوامل يمكن تحليلها مرة أخرى. توقف عن التحليل عندما تصبح كل العوامل أرقام أولية. تحليل الأعداد السالبة يكون بالطريقة نفسها.