What is the prime factorization of 93? I need a breakdown on how to do it not just the answer?

Answer 1

93 = 3 × 31
93, find the divisor
it is not divisible by 2
sum of digits 9 + 3 = 12 divisible by 3 hence 93 divisible by 3
another divisor is 31 is prime number so factors are 3 × 31

Answer 2

When finding prime factorizations, you need to just start dividing the number by possible factors. There are a few things you probably already know like:

1. Any even number is divisible by 2

2. Any number ending in 5 or 0 is divisible by 5

Here are a few other fqacts that will help you.

3. You only need to divide by prime numbers

4. You only need to test numbers less than the square root of the value you ar testing.

5. If you take all the digits of a number and add them up, then if that number is divisible by three -- so is your original number

6. If you take all the digits of a number and add them up, then if that number is divisible by nine-- so is your original number


Let's use these rules here. The number is 93. That is less than 100 & the square root of 100 is ten, so we only need to consider factors less than ten.

The only prime numbers less then ten are 2, 3, 5, and 7.

We can add the digits of 93 ==> 9+3 = 12. 12 is divisible by three -- so our original number is dividible by three (note -- if we didn't know that, we could add the digits of 12 together ==> 1+2 = 3 ).

So -- we can divide 93 by 3 to get: 93 = 3*31.

31 is a prime number. If you didn't know that, you could notice that 31 < 36 -- so you would only have to try to divide it by the prime numbers less than six.

Answer 3

First step...find a number that will divide evenly into 93. The obvious one that jumps out at me is 3, which goes in 31 times. So our factorization so far is 3*31.

Now examine each of the factors in turn:

Is three a prime number, or can it be further factored? It's prime. So we're done with it.

Is 31 a prime number or can it be further factored? It's also prime. So we're done with it as well.

Since all of our factors are prime numbers, we are confident that 3*31 is the prime factorization of 93.

Answer 4

93=3x31

Answer 5

3,31