Questions: Write 75 as a product of prime factors.

Solution Steps

To write 75 as a product of prime factors, we need to find the prime numbers that multiply together to give 75. We start by dividing 75 by the smallest prime number (2) and continue with the next smallest primes (3, 5, 7, etc.) until we reach 1.

To express $75$ as a product of prime factors, we start by dividing $75$ by the smallest prime number, which is $2$. Since $75$ is odd, we move to the next prime number, $3$.

Dividing $75$ by $3$: $$75 \div 3 = 25$$ Next, we factor $25$ by dividing it by the smallest prime number, $5$: $$25 \div 5 = 5$$ Finally, we divide $5$ by $5$: $$5 \div 5 = 1$$

The prime factors we found are $3$ and $5$. Since $5$ appears twice in the factorization, we can express $75$ as: $$75 = 3 \times 5 \times 5 = 3 \times 5^2$$

Final Answer