What is a prime factorization?

Answer 1

Prime factorization is finding the prime factors you need to multiply together to get the original number. A prime factor is a factor that is a Prime number.

Example:

The prime factorization of 30 is 2 x 3 x 5
Prime factorization is breaking a number into smaller prime divisors which multiply to equal the original number.
All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.

Example: 210

210 Divide by two.

105,2 Divide by three.

35,3,2 Divide by five.

7,5,3,2 Stop. All the factors are prime.

2 x 3 x 5 x 7 = 210

That's the prime factorization of 210.

Answer 2

A prime number is a number which cannot be divided by any number, other than itself and 1,

without leaving a remainder.

The first few prime numbers are 2, 3, 5, 7 11, 13, 17, 19, 23, 29, 31 and so on...

A factor is a number which, when multiplied by another number, will give a third number.... such as 10 and 4 are factors of 40; or 25 and 6 are factors of 150.

However none of those factors are 'prime factors' - those are prime numbers which are factors of other numbers.

The prime factors of 40 are 2, 2, 2 and 5. The three 2s are listed separately because you need to multiply 2 by 2 to get 4, and by 2 again to get 8. Then multiplying that by 5 gives 40.

Similarly, the prime factors of 150 are 2, 3, 5 and 5... as 2 by 3 gives 6. 6 by 5 gives 30 and 30 by 5 gives us 150.

In short, prime factors of a number are the smallest numbers which when multiplied together give us that number, and which themselves are not capable of being evenly divided.
it is a number than can only be divisble by 1. these numbers are numbers like 1,2,3,5,7,11,13,17,19... etc...

Answer 3

Any number can be broken down, or factored, into smaller and smaller factors which multiply to give the original number, when you have reached the smallest possible factors, then those factors will be prime, all those factors together constitute the prime factorization of that number.