To factor the number, it is necessary to clarify whether the number is compound, since the process of decomposition is the division of a composite number into primes.
A prime number is only divisible by 1 and into itself.
And the unit is neither a simple nor a compound number.
To simplify the process and obtain a quick result, you need to know the signs of dividing numbers by 2, by 3, by 5, by 10, etc.
You will need
If the number is small, then such a decomposition is simpleDo based on the multiplication table. For example, we need to factor the number 6. It is known that 6 = 2 x 3. The numbers 2 and 3 are simple, respectively, these numbers are prime factors of the number 6. For the expansion of the number 49, we get 7 and 7, since 49 = 7 x 7.
When a large number is first to be dividedIts on the smallest prime number, which is its divisor. And so on, until the full result is obtained. For example, you want to expand the number 242 into prime factors. The smallest divisor of this number is number 2. We get: 242: 2 = 121. Next, we search for the smallest divisor of the number 121. It is obvious that this number is not divisible by 2, 3, 5 or 7. Thus, we sort out the prime numbers by their ascending. The number 121 is divisible by 11. We get: 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 the compound number 242 are the numbers 2, 11 and 11 This can be written in the form of a product: 242 = 2 x 11 x 11 or 242 = 2 x 11 ^ 2.
To simplify the decomposition problem, we canUse the table of prime numbers. By the table we search for the smallest divisor by the search method. Divide the given number into it and then, in the same way, search for the smallest divisor of the obtained number. Such actions are performed until the result is a simple number. For example, you need to expand the number of prime factors into a number of 1454. We look at the table. In the first place number 2. It suits us: 1738: 2 = 869. Next, on the table we look for the number to which the 869 is divided. Using the signs of the divisibility of numbers, it becomes obvious that this is 11. 869: 11 = 79. And the number 79 is Simple, it can be seen from the table. It follows that the prime factors of the number 1738 are 2, 11 and 79. The result can be written in the form: 1738 = 2 x 11 x 79.