Math Snap

STEP 1

1. We need to express $1,200$ as a product of prime numbers.
2. The prime factorization should include exponents for repeated prime factors.

STEP 2

1. Identify the smallest prime factor.
2. Divide the number by its smallest prime factor.
3. Repeat the process with the quotient until the quotient is 1.
4. Write the prime factorization using exponents.

STEP 3

Identify the smallest prime factor of $1,200$. The smallest prime number is $2$.

STEP 4

Divide $1,200$ by $2$ repeatedly until it is no longer divisible by $2$.
$$1,200 \div 2 = 600$$ $$600 \div 2 = 300$$ $$300 \div 2 = 150$$ $$150 \div 2 = 75$$ Now, $75$ is not divisible by $2$.

STEP 5

Identify the next smallest prime factor of $75$, which is $3$.
Divide $75$ by $3$ until it is no longer divisible by $3$.
$$75 \div 3 = 25$$ Now, $25$ is not divisible by $3$.

STEP 6

Identify the next smallest prime factor of $25$, which is $5$.
Divide $25$ by $5$ repeatedly.
$$25 \div 5 = 5$$ $$5 \div 5 = 1$$

Write the prime factorization using exponents. Count the number of times each prime factor appears:
- $2$ appears $4$ times.
- $3$ appears $1$ time.
- $5$ appears $2$ times.
Thus, the prime factorization of $1,200$ is:
$$2^4 \times 3^1 \times 5^2$$ The prime factorization of $1,200$ is:
$$\boxed{2^4 \times 3 \times 5^2}$$