To expand the number of factoring, it is necessary to clarify whether a number is composite, since the process of decomposition - this division is a composite number into prime numbers.
A prime number is divisible only by 1 and itself.
Wherein the unit is neither simple nor composite number.
To simplify the process and to obtain a quick result is necessary to know the signs of division numbers 2, 3, 5, 10, etc.
You will need
If the number is small, it is simply the decompositiondone on the basis of the multiplication table. For example, it is required to factor the number 6. It is known that the 6 x 2 = 3. The numbers 2 and 3 prime respectively, and these numbers are the prime factors of the decomposition of 6. 7 and 49 obtain 7 as 7 x 49 = 7.
With a large number must first divideit on the smallest prime number that is a divisor of it. And so on, until the full results. For example, the need to expand the number 242 into simple factors. The smallest divisor of this number - the number 2. Get the 242: 2 = 121. Next, look for the smallest divisor of 121. It is obvious that any 2 or 3 or 5 or 7 this number is not divisible. So, we sort out the prime numbers in their ascending order. The number 121 is divisible by 11. So we have: 121: 11 = 11. The number 11, of course, is only divisible by 11. So, 11: 11 = 1. As a result, we find that the prime factors of composite numbers 242 are numbers 2, 11 and 11 . This can be written as the product of: 242 = 2 x 11 x 11 or 242 x 11 = 2 ^ 2.
To simplify the problem may be expansionsuse the table of prime numbers. According to the table looking for the smallest divisor method busting. Divide this number on it and then, by the same method to find the smallest divisor of the resulting number. Such actions are performed as long as the result does not get a prime number. For example, you must be decomposed into prime factors of the number of 1454. Refer to the table. In the first place the number 2. It suits us: 1738: 2 = 869. The following table looking at the number by which to divide 869. Using signs of divisibility of numbers, it becomes clear that this is - 869 11: 11 = 79. And the number 79 is simple, it can be seen from the table. It follows that the prime factors of 1738 are 2, 11 and 79. The result can be written as: 1738 = 2 x 11 x 79.