What is the prime factorization of 360?

Divide by the smallest primes. $360=8\cdot45=2^3\cdot45$, and $45=9\cdot5=3^2\cdot5$, so $360=2^3\cdot3^2\cdot5$, choice F. Check: $8\cdot9\cdot5=360$. Choice G ($2^2\cdot3^3\cdot5$) equals $540$, since the exponents of $2$ and $3$ are swapped. Choice H ($2^3\cdot3\cdot5^2$) equals $600$. Choice J ($2^4\cdot3^2$) equals $144$ and omits the factor of $5$. A prime factorization must multiply back to the original number, which is the simplest check. Dividing repeatedly by $2$, then $3$, then $5$ shows each prime factor in turn: $360, 180, 90, 45, 15, 5, 1$ uses three twos, two threes, and one five.