Write the prime factorization of 84.
Understand the Problem
The question is asking us to break down the number 84 into its prime factors, which means identifying the prime numbers that multiply together to give 84.
Answer
$2^2 \times 3^1 \times 7^1$
Answer for screen readers
The prime factorization of 84 is $2^2 \times 3^1 \times 7^1$.
Steps to Solve
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Start with the number Begin with the number 84 that needs to be factorized into its prime components.
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Divide by the smallest prime number Start dividing 84 by the smallest prime number, which is 2: $$ 84 \div 2 = 42 $$
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Continue dividing by 2 Since 42 is also even, we can divide by 2 again: $$ 42 \div 2 = 21 $$
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Move to the next smallest prime number Now, since 21 is odd, we move to the next smallest prime number, which is 3: $$ 21 \div 3 = 7 $$
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Identify the final prime number The last number you get is 7, which is a prime number itself, so we stop here.
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Compile the prime factors Now we can compile all the prime factors we found: The prime factors of 84 are $2, 2, 3,$ and $7$. We can write this as: $$ 84 = 2^2 \times 3^1 \times 7^1 $$
The prime factorization of 84 is $2^2 \times 3^1 \times 7^1$.
More Information
The prime factorization of a number is useful in various areas, such as simplifying fractions or finding the greatest common divisor. The number 84 is also notably the product of two consecutive integers, $7 \times 12$.
Tips
- Forgetting to check divisibility by smaller prime numbers before moving to larger primes. Always start with the smallest prime, which is 2.
- Not recognizing that 1 is not a prime number. Every factor should be a prime.
