What is the prime factorization of 18 and 20?

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To get the prime factorization of a number, apply divisibility rules.

(a) 18

Since 18 is an even number, it is divisible by the smallest even number which is 2 (`18-:2=6` ). So,

`18 = 2 xx 9`

Then, factor 9 further. Since 9 is an odd number and a...

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To get the prime factorization of a number, apply divisibility rules.

(a) 18

Since 18 is an even number, it is divisible by the smallest even number which is 2 (`18-:2=6` ). So,

`18 = 2 xx 9`

Then, factor 9 further. Since 9 is an odd number and a multiple of 3, then it is divisible by 3 (`9-:3=3` ).

`18 =2xx3xx3`

Now that factors are all prime numbers, express the repeated factors in exponent form.

Therefore, `18=2xx3^2` .

(b) 20

20 is an even number. So,applying the divisibility rule for even numbers, its factor will be:

`20=2xx10`

10 is an even number too. So it can be factor further by applying the same rule.

`20=2xx2xx5`

Now that the factors are all prime numbers, express the repeated factors in exponent form.

Thus, `20=2^2xx5` .

Approved by eNotes Editorial Team

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