Answer
$2^{2}\times3^{2}\times5$
Work Step by Step
A number is prime if it has only two factors: 1 and itself.
We know that the factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
2 is a prime number, so we can divide 180 by 2
$180\div2=90$
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. Since 2 is a prime number, divide by 2.
$90\div2=45$
The factors of 45 are 1, 3, 9, 15 and 45. Since 3 is a prime number, divide by 3.
$45\div3=15$
The factors of 15 are 1, 3, 5, and 15. Since 3 is a prime number, divide by 3.
$15\div3=5$
5 is also a prime number
Therefore, the prime factorization of 180 is $2\times2\times3\times3\times5=2^{2}\times3^{2}\times5$.
