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.
Factorization into its smallest factors.
The prime factorization is... 2x2x2x2x2x5x5
Prime Factorization of 9 and 15The prime factorization of 9 is:3 X 3The prime factorization of 15 is:3 X 5
find the prime factorization of 268
The prime factorization of 186 is 2,3,31,168
255 85,3 17,5,3 3 x 5 x 17 = 255
The square root of 729 is 27 and as a product of its prime factors in exponents it is 36
When asked for a factorization, it is generally understood to mean the prime factorization.
1001 Divide by seven. 143,7 Divide by eleven. 13,11,7 Stop. 7 x 11 x 13 = 1001
Since 62 is even, divide by 2. Since the result is prime, stop. 2 x 31 = 62
Factorization of 150 = 2x3x5x5.
Factorization into its smallest factors.
43 is prime; no factorization.
Factorization of 91The factorization of 91 is:1 X 917 X 13
Prime Factorization of 217The prime factorization of 217 is:7 X 31
Factorization Form of 91The factorization form of 91 is 7 X 13.
When all the factors are prime numbers, that's a prime factorization.