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HOW decomposed into prime factors

How to decompose into prime factors

Any composite number can be written as the product of prime numbers. This representation is called the factorization.

Factoring is useful for reducing fractions.

You will need

  • - A table of prime numbers



Put in front of a table of prime numbers. Prime numbers - numbers that in integer division divisible only by themselves and One unit.


Look for a prime table, which wasI would divisor for a given composite number. Use well-known signs of divisibility of numbers, or simply try to share a simple composite number.


Once you have found a divider, divide the compositenumber on it. Then continue to search for prime factor for the resulting quotient. Start again from the beginning of the table. Continue the process until a prime number not yet will result in fission. Write it down and prime divisors found earlier.


For example, decompose into simple multipliers the number in 1197. On the basis of the divisibility of numbers divided by 3 since the sum of numbers in it 1 + 1 + 9 + 7 = 18 is divisible by 3 and even 9. Thus, the first two prime divisors 3 and 3, divide the number of them: 1197: 3 = 399, 399: 3 = 133. Now looking for a prime divisor for the number 133. Obviously, it is not divisible by 2, 3 and 5, try to divide by 7. it will turn 133: 7 = 19. As a result of dividing the obtained prime number 19, so that the expansion is completed, and is as follows: 1197 = 3 * 3 * 7 * 19.

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