what is the prime factorization of 304
I noticed that 304's last digit is 4.
Then I noticed that if you have a whole number of things
and that whole number ends in either a 2,4,6,8, or 0 then
you can split your things up into two equal piles or groups.
So we call such numbers as that "even" numbers. But if you have
an odd number of things to divide up, you'll have to cut one
thing in two to do it.
What we want to do is to keep dividing until we can divide no
more. But we never divide a number by itself or by 1. That's
because if we divide a number by itself we get 1, and if we
divide a number by 1 we get itself, i.e., the same number back.
So we're getting nowhere, so we avoid that in our division. 1
is not considered a prime. But it was once considered prime.
In the old Chemical Rubber Co. mathematical tables, 1 was listed
in the table of primes. There is a reason why mathematicians
stopped considering 1 to be prime, but I won't go there.
Anyway,
Hey, 304 ends in a 2
So I'll divide it by 2
I get 152
So 304 = 2*152
Hey, 152 ends in a 2
So I'll divide it by 2
I get 76
So 304 = 2*2*76
Hey, 76 ends in a 6
So I'll divide it by 2
I get 38
So 304 = 2*2*2*38
Hey, 38 ends in a 2
So I'll divide it by 2
I get 19
So 304 = 2*2*2*2*19
Oh! Oh! We've come to a halt. We can't divide 19 by anything except 1.
Not only is 19 odd, but it's also prime.
So that's the factorization of 304 into prime numbers:
304 = 2*2*2*2*19
So 304 = 2*2*2*2*19
And now we're stuck. This roller coaster came to a halt.
That's it:
2*2*2*2*19 is the prime factorization of 304.
Edwin
