Express 60 as the product of its prime factors.
The correct answer and explanation is:
To express 60 as the product of its prime factors, start by finding the prime numbers that multiply together to give 60.
- Begin by dividing 60 by the smallest prime number, 2. Since 60 is even, it is divisible by 2: 60÷2=3060 \div 2 = 30
- Next, divide 30 by 2, since it is still even: 30÷2=1530 \div 2 = 15
- Now, 15 is not divisible by 2, so move on to the next smallest prime number, which is 3. Divide 15 by 3: 15÷3=515 \div 3 = 5
- The number 5 is already a prime number, so we stop here.
Thus, the prime factorization of 60 is: 60=2×2×3×560 = 2 \times 2 \times 3 \times 5
Or, written more concisely: 60=22×3×560 = 2^2 \times 3 \times 5
Explanation:
Prime factorization is the process of breaking down a number into its prime factors. Prime numbers are numbers greater than 1 that can only be divided by 1 and themselves. By continuously dividing the number by the smallest prime possible, you reduce the original number until only prime numbers remain. This method ensures that you find the simplest set of factors that multiply together to form the original number. In this case, by dividing 60 by 2, 3, and 5, you reach the prime factorization 22×3×52^2 \times 3 \times 5, showing that 60 is made up of these prime factors.