Write 84 as a product of prime factors.
Understand the Problem
The question is asking to express the number 84 as a product of its prime factors. This means we need to find the prime numbers that can be multiplied together to give the original number 84.
Answer
The prime factorization of 84 is \( 2^2 \times 3^1 \times 7^1 \).
Answer for screen readers
The prime factorization of 84 is ( 2^2 \times 3^1 \times 7^1 ).
Steps to Solve
-
Divide by the smallest prime number
Start by dividing 84 by the smallest prime number, which is 2. $$ 84 \div 2 = 42 $$ -
Continue dividing by 2
Since 42 is still even, divide it again by 2. $$ 42 \div 2 = 21 $$ -
Next prime number
Now, we need to check if 21 can be divided by the next prime number, which is 3. $$ 21 \div 3 = 7 $$ -
Identify the last prime factor
The result, 7, is a prime number itself, so we can stop here. -
Write down the prime factorization
Putting it all together, we express 84 as a product of its prime factors: $$ 84 = 2^2 \times 3^1 \times 7^1 $$
The prime factorization of 84 is ( 2^2 \times 3^1 \times 7^1 ).
More Information
The prime factorization shows the building blocks of the number 84. Prime factorization is useful in various areas of mathematics, including simplifying fractions and finding the least common multiple (LCM) and greatest common divisor (GCD).
Tips
- Forgetting to check divisibility by the next smallest prime after dividing.
- Stopping after finding one prime factor without fully factoring the number.
To avoid these mistakes, always ensure you've divided by all applicable primes until reaching a prime number.
