how many prime factors are there in prime factorization of 5005
Answers
#BAL
5005 is not even, so its not evenly divisible by 2 (the first prime number). Testing for divisibility by 3 (the next prime number) is easy, add up the individual digits of 5005, 5 + 0 + 0 + 5 = 10, then doing it again 1 + 0 = 1. 1 is not divisible by 3, so neither is 5005.
The next prime number is 5, and testing for divisibility by 5 is easy, any number that ends in 5 or 0 is evenly divisible by 5 while others are not. 5005 ends in 5, so it is divisible by 5, the answer there is 1001, so at this point we have 5 * 1001. If 1001 were prime we’d be done, but to find out we need to keep testing. 2 and 3 have already been tested for so they don't need to be tested again, so we start again at 5. 1001 ends in 1 so it is not evenly divisible by 5.
Testing for 7 there is no rule, so the calculator needs to be used, and it turns out that 1001 = 7 * 143. At this point for the factorization we have 5005 = 5 * 7 * 143. Testing again for 7, 143 / 7 = 20.4285… so there is not a second 7.
The next prime number is 11, and the rule for 11 is a little more complicated, add up the odd digits and the even digits and compare them. There are two odd digits (1 and 3) so the sum there is 4; there is only one even digit, a 4 so the sum is again 4. The two numbers are equal, so 143 is divisible by 11. The answer there is 143 = 11 * 13. 13 is a prime number so we are done.
The complete factorization is 5005 = 5 * 7 * 11 * 13, so we can see that there are 4 prime numbers.
By the way, the tests that I used above can tell if a number is evenly divisible, but not what number its divisible by. So if the test comes back positive, you still need to do the complete division (by hand or by calculator, whichever) but if it comes back negative then you know that you don't need to do the division.