Write the prime factorization of each number. 93
The Correct Answer and Explanation is:
To find the prime factorization of 93, we need to express it as a product of prime numbers. Here’s the step-by-step process:
Step 1: Check for divisibility by 2
93 is an odd number, so it is not divisible by 2. We move on to the next prime number.
Step 2: Check for divisibility by 3
Next, check if 93 is divisible by 3. A quick rule for divisibility by 3 is to sum the digits of the number. For 93, the sum of the digits is 9 + 3 = 12, and since 12 is divisible by 3, 93 is divisible by 3.
Now, divide 93 by 3:
93÷3=3193 ÷ 3 = 3193÷3=31
Step 3: Check if 31 is a prime number
We are left with 31. To check if 31 is prime, we need to verify that it is not divisible by any prime numbers smaller than itself. The prime numbers less than 31 are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. Since 31 is not divisible by any of these primes, 31 is a prime number.
Step 4: Conclusion
Now that we’ve broken down 93 into its prime factors, the prime factorization of 93 is:
93=3×3193 = 3 × 3193=3×31
Explanation
The prime factorization of a number is a way to express the number as the product of primes. Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. In this case, 93 is divisible by 3, which is the first prime factor we find. Dividing 93 by 3 leaves 31, a prime number. Since 31 cannot be divided any further by smaller primes, the prime factorization stops there.
Thus, the prime factorization of 93 is:
93=3×3193 = 3 × 3193=3×31
