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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.

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A prime factor is a factor that is a Prime number.

3 is a prime factor of 12.

4 is a composite factor of 12.

Q: What is a prim factorization?

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115 = 5 × 23

144 = 24 × 32

140 = 22 × 5 × 7

18 = 2 x 3 x 3

5 x 5 x 5 x 11

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19 is already prime; no factorization.

2x2

No.

43 is already prime; no factorization required.

Prime Factorization: 2*5*31

No it isn't. 235/5 = 47 and 47 is a prim number. 235 isn't a prime number so it isn't a prim factorization. The real factorization is 47 * 5.

It is: 2*29 = 58

67 is a prime number

144 = 24 × 32

2 x 3

216 = 23 × 33

It is: 2, 3 and 7