What times what equals 216
The Correct Answer and Explanation is :
To solve for what times what equals 216, let’s first look at its factors.
216 is the product of (6 \times 6 \times 6) or (6^3), which means 6 multiplied by itself three times equals 216. However, if we’re looking for two numbers that multiply to give 216, several pairs can work, depending on which factors we choose.
Explanation
- Prime Factorization: To understand all possible factors, it helps to break 216 down into its prime factors. 216 can be written as:
[
216 = 2^3 \times 3^3
]
This breakdown shows that 216 is divisible by powers of both 2 and 3. Knowing the prime factors helps identify all possible pairs of numbers that could multiply to 216. - Possible Factor Pairs:
We can pair different factors of 216 to get products that equal it. Here are some possible pairs:
- (1 \times 216)
- (2 \times 108)
- (3 \times 72)
- (4 \times 54)
- (6 \times 36)
- (9 \times 24)
- (12 \times 18)
- Square Root Factorization:
To find two identical numbers that equal 216 when multiplied isn’t possible because 216 isn’t a perfect square. However, knowing that 6 multiplied by itself three times gives 216 is useful in contexts involving cubes or powers. - Application of Factor Pairs:
These factor pairs are useful in many real-world situations, such as dividing a space into sections, calculating area or volume, or breaking down a number into manageable parts for multiplication.
So, if asked for two numbers that multiply to 216, any of the pairs listed above would work depending on the context.