repeated division by smallest prime numbers.
divide by 2 .. 108
divide by 2 again.. 54
divide by 2 again.. 27
divide by3 .. 9
divide by 3 again .. 3
so 2x2x2x3x3x3
Chat with our AI personalities
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
LCM of 27 36 54 is 108.
What is the prime factorization of 256^180
3 is already prime. No factorization.