To find the prime factorization of the number 84, we can follow these detailed steps:
1. Start with the smallest prime number, which is 2.
- Check if 84 is divisible by 2. Since 84 is even, it is divisible by 2.
- Divide 84 by 2 to get 42. The quotient is 42.
- Write down 2 as a factor and continue with the quotient.
2. Continue dividing by 2 as long as the quotient is even.
- Check if 42 is divisible by 2. Since 42 is even, it is divisible by 2.
- Divide 42 by 2 to get 21. The quotient is 21.
- Write down another 2 as a factor and continue with the quotient.
3. Move to the next smallest prime number, which is 3.
- Check if 21 is divisible by 3. Since the sum of the digits of 21 (2 + 1 = 3) is divisible by 3, 21 is divisible by 3.
- Divide 21 by 3 to get 7. The quotient is 7.
- Write down 3 as a factor and continue with the quotient.
4. Move to the next smallest prime number, which is 7.
- Check if 7 is a prime number. Since 7 is only divisible by 1 and 7, it is a prime number.
- Write down 7 as the final factor.
Putting all the factors together, we get:
[tex]\[ 84 = 2 \times 2 \times 3 \times 7 \][/tex]
Therefore, the prime factorization of 84 is:
[tex]\[ 2, 2, 3, 7 \][/tex]
