# How many prime factors does 144 have?

Dec 16, 2016

It depends on how we are counting prime factors. (If you are in a class, the instructor may have already talked about how they want you to count them.)

#### Explanation:

$144 = 2 \times 2 \times 2 \times 2 \times 3 \times 3$

$144$ has two distinct (or two different) prime factors.

Without the word "distinct" or "different" or something else to indicate how to count, I would say $144$ has six prime factors. (Four of them are $2$'s and two of them are $3$'s.)

Dec 16, 2016

There are 6 prime numbers in the number 144

#### Explanation:

Prime factors are part of a number that cannot be separated and broken down.
We have a number 144. This can still be divided.
you divide your number and you get 12 on each side. as 12x12=144
you then have to divide 12 and you get 3x4 on each side
since you have a 3, this is a prime number because it cant be divided.
But you still have 4. That can be divided by 2 as 2x2=4
Make yourself a diagram.

...................................144
........................12....................12
................ 3 ..........4......... 3 .........4
....................... 2 ........ 2 .......... 2 ....... 2

Now counting how many prime numbers are in 144, I bold the numbers that can not be divided.
$3 \times 2 \times 2 \times 3 \times 2 \times 2$
Therefore there are 6 prime numbers in the numbers 144

Dec 16, 2016

$144 = \textcolor{red}{2} \times \textcolor{red}{2} \times \textcolor{red}{2} \times \textcolor{red}{2} \times \textcolor{b l u e}{3} \times \textcolor{b l u e}{3}$

#### Explanation:

Depending on how you want to count, 144 can have two ( $\textcolor{red}{2}$ and $\textcolor{b l u e}{3}$) or six ( four $\textcolor{red}{2}$s and two $\textcolor{b l u e}{3}$s) prime factors.

Dec 19, 2016

$2 \times 2 \times 2 \times 2 \times 3 \times 3 = {2}^{4} \times {3}^{2}$

#### Explanation:

Always work your way up from the smallest prime number until you have completely split the original number up into all primes.

Test for 2,3,5,7,11,13,17 and so on. If you prefer you can always sketch a prime factor tree.

Mar 6, 2017

$144$ has two prime factors.

(They are 2 and 3)

#### Explanation:

The question is not really clear.

There are many way that questions about factors can be asked:

• "How many factors does $144$ have?"
There are $15$ factors.

• "List the factors of $144$" $1 , 2 , 3 , 4 , 6 , 8 , 9 , 12 , 16 , 18 , 36 , 48 , 72 , 144$

• "How many prime factors does $144$ have"
There are two prime factors.

• "List the prime factors of $144$
$2 , 3$

• "Write $144$ as the product of its prime factors"
$144 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3$

Note that the question "How many?" has a number answer, without any details being required.

("How many people were on the bus?" does not require all their names, just the fact that there were 19 people.)