What is the prime factorization of 385?

Steps to Solve

1. Start with the number 385

We begin by checking if 385 can be divided by the smallest prime number, which is 2. Since 385 is odd, it is not divisible by 2.

2. Check divisibility by the next prime, 3

Next, we check if 385 can be divided by 3. To do this, we add the digits of 385: $3 + 8 + 5 = 16$. Since 16 is not divisible by 3, 385 is not divisible by 3.

3. Check divisibility by the next prime, 5

We check if 385 can be divided by 5. Since the last digit of 385 is 5, it is divisible by 5. We perform the division:

$$ 385 \div 5 = 77 $$

4. Factor the result, 77

Now, we factor 77. The smallest prime number to check is again 2. Since 77 is odd, it’s not divisible by 2. Next, we check 3, which doesn't work either (as shown before). Now we check 5, and since 77 doesn't end in 0 or 5, it's also not divisible by 5. Next, we check 7:

$$ 77 \div 7 = 11 $$

5. Prime check for 11

Finally, we check if 11 is a prime number. It's only divisible by 1 and itself, confirming that 11 is a prime number.

6. Combine all the prime factors

Now we have factored 385 into primes:

$$ 385 = 5 \times 7 \times 11 $$