Write the Prime Factorization of 36 in exponent form. Use exponents when necessary and order the factors from least to greatest (Example:

3

Prime factorization of a number can be found by simply factoring out prime numbers from the given number until it becomes 1. In other words, divide the given number 2 and then do the same with the quotient until the quotient is not divisible by 2. Then repeat the process with 3, 5 and so on with until the divisor becomes 1.

Now to express the prime factorization in exponent form, simply count the number of times each prime number repeats in the prime factorization and that becomes the exponent on that prime factor in the exponent form of the prime factorization of the number.

Step 1 - Write the prime factorization in the expanded form

In order get the prime factorization of 36, first divide it by 2, then we get 18, divide 18 by 2, we get 9. 9 is not divisible by 2, so we move on to 3. 9 when divided by 3 leaves 3, now 3 divided by 3 leaves 1. So we stop.

`36 = 2 xx 2 xx 3 xx 3`

Step 2 - Write the prime factorization in the exponent form

We notice that there are two 2s and two 3s in the prime factorization of 36, so its exponent form is

`36 = 2^2 xx 3^2`

Concept Knowledge , Arithmetic