First, the square root of 210 is less than 15, so the tools we will need are the prime numbers less than 15. These are: 2, 3, 5, 7, 11, and 13.
To begin, we will divide 210 by 2.
210/2 = 105, which is an integer, so write "2" and continue.
Now we try 3.
105/3 = 35, which is also an integer, so write "3" and continue.
Now we try 5.
35/5 = 7, which is also an integer, so write "5" and continue.
We know 7 is prime...
Working backwards, we have 210 = 2*3*5*7.
Note that if one of these did not divide 210, we would have to skip it and "try again" with the next known prime. If none divided 210, then 210 would be prime.
All numbers (except for 1 and 0) have prime factors. Sometimes the prime factors are repeated. The prime factorization of 216 is 2 x 2 x 2 x 3 x 3 x 3. The distinct prime factors of 216 are 2 and 3.
Think of the "ex" in index as meaning exponent. Write the prime factorization with exponents. 216 = 23 x 33
3 is already prime. No factorization.
What is the prime factorization of 256^180
113 is already prime. No factorization.
23 x 33 = 216
23 x 33 = 216
The prime factors for 216 are 2,2,2,3,3, and 3. 2 x 2 x 2 x 3 x 3 x 3 = 216
Use a factor tree. 216 108,2 54,2,2 27,2,2,2 9,3,2,2,2 3,3,3,2,2,2
The prime factorization of 216 is 2,2,2,3,3,3 or 2 x 2 x 2 x 3 x 3 x 3. Prime factorization is finding prime numbers that multiplies together to satisfy the product. In your case, the product is 216.
2 x 2 x 2 x 3 x 3 x 3 = 216
2 x 2 x 2 x 3 x 3 x 3 = 216 23 x 33 = 216
216 = 23 × 33
It is: 72
All numbers (except for 1 and 0) have prime factors. Sometimes the prime factors are repeated. The prime factorization of 216 is 2 x 2 x 2 x 3 x 3 x 3. The distinct prime factors of 216 are 2 and 3.
You've come to the right place. Here is the answer: 216 = 2 x 2 x 2 x 3 x 3 x 3
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: 216 216 Divide by two. 108,2 Divide by two. 54,2,2 Divide by two. 27,2,2,2 Divide by three. 9,3,2,2,2 Divide by three. 3,3,3,2,2,2 Stop. All the factors are prime. 2 x 2 x 2 x 3 x 3 x 3 = 216 Repeated factors can be abbreviated by the use of exponents (powers). 23 x 33 = 216 That's the prime power factorization of 216.