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How to Find the Prime Factorization of 16 with Exponents
Mathematics
Grade 6
Question Content
Write the prime factorization of 16. Use exponents when appropriate and order factors from least to greatest (for example, 2²·3·5).
Correct Answer
2⁴
Detailed Solution Steps
1
Step 1: Start by dividing the number 16 by the smallest prime number, which is 2. 16 ÷ 2 = 8.
2
Step 2: Divide the result 8 by 2 again: 8 ÷ 2 = 4.
3
Step 3: Divide 4 by 2 once more: 4 ÷ 2 = 2.
4
Step 4: Divide 2 by 2: 2 ÷ 2 = 1. We stop when we get 1 as the result.
5
Step 5: Count how many times we divided by 2: we did it 4 times. So we can write this as 2 raised to the 4th power, or 2⁴, which is the prime factorization in ordered, exponential form.
Knowledge Points Involved
1
Prime Number
A prime number is a whole number greater than 1 that has exactly two distinct positive divisors: 1 and itself. Examples include 2, 3, 5, 7. These are the building blocks for prime factorization.
2
Prime Factorization
Prime factorization is the process of breaking down a composite number into a product of prime numbers. This product represents the unique set of primes that multiply together to equal the original number.
3
Exponents in Prime Factorization
When a prime factor is repeated multiple times in a prime factorization, we use exponents to simplify the expression. The exponent tells us how many times the prime factor is multiplied by itself. For example, 2×2×2×2 is written as 2⁴.
4
Ordering Prime Factors
When writing prime factorization, we list the prime factors from the smallest to the largest value. This standard order makes the factorization consistent and easy to read and compare with other factorizations.
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