What times what equals 216?

Steps to Solve

1. Find the prime factorization of 216

To find the factors of 216, we first need its prime factorization. We can divide 216 by the smallest prime number, which is 2.

$$ 216 \div 2 = 108 $$

Continuing to divide by 2, we have:

$$ 108 \div 2 = 54 $$

And again,

$$ 54 \div 2 = 27 $$

Now, we can no longer divide by 2, so we move to the next prime number, which is 3:

$$ 27 \div 3 = 9 $$

Dividing 9 by 3 gives us:

$$ 9 \div 3 = 3 $$

Finally, 3 divided by 3 results in:

$$ 3 \div 3 = 1 $$

The prime factorization of 216 is:

$$ 216 = 2^3 \times 3^3 $$

2. Identify the factors of 216

Using the prime factorization $2^3 \times 3^3$, we can find the factors. The factors of a number can be found by taking various combinations of its prime factors.

The factors of 216 are:

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, and 108, 216.

3. Identify pairs that multiply to 216

Now, we find pairs of these factors that yield 216 when multiplied:

• (1 \times 216)
• (2 \times 108)
• (3 \times 72)
• (4 \times 54)
• (6 \times 36)
• (8 \times 27)
• (9 \times 24)
• (12 \times 18)

Therefore, the possible pairs of numbers that multiplied together equal 216 are identified.