What 3 numbers can you multiply to get 252 as your product
The Correct Answer and Explanation is :
To find three numbers that multiply to give a product of 252, we can break down the number into its prime factors and then look for combinations. The prime factorization of 252 is:
[ 252 = 2^2 \times 3^2 \times 7 ]
From this factorization, we can explore different combinations of the prime factors to arrive at three numbers. One straightforward combination is:
1. 3, 7, and 12
Explanation
- Finding Prime Factors: The first step in solving the problem is to find the prime factorization of 252. As noted above, it breaks down to ( 2^2 \times 3^2 \times 7 ). This means that 252 can be expressed as the product of its prime factors, which gives us flexibility in choosing different combinations.
- Choosing Combinations: To find three numbers, we can group the factors in various ways. One combination is to take the factors 3, 7, and the product of the remaining factors, which is ( 2^2 \times 3 = 12 ). Thus, we have: [
3 \times 7 \times 12 = 252
] - Verifying the Product: It’s essential to verify that the chosen numbers indeed multiply to 252: [
3 \times 7 = 21
]
[
21 \times 12 = 252
] - Alternative Combinations: Other combinations can be explored as well. For example, ( 2 \times 6 \times 21 ) also results in 252, where ( 6 ) is derived from ( 2 \times 3 ).
- Conclusion: Thus, multiple sets of three numbers can yield a product of 252. However, a clear example is 3, 7, and 12, which illustrates how we can manipulate the prime factors to derive valid combinations. This process not only showcases the versatility of prime factorization but also enhances problem-solving skills in multiplication.
In summary, ( 3 \times 7 \times 12 = 252 ) is a valid and illustrative combination of three numbers resulting in the specified product.