Write 84 as a product of a prime number

For small numbers, just try every prime less than the square root. Why stop there, because if there are two factors, and one is greater than the square root, the ther must be less than the square root, and you will already have tried it.

For example try 2 as a factor of 84.

84 = 2*42

Now, try 2 as a factor of 42.

84 = 2*2*21

Since 21 is odd, it will have no even factors. So, try 3, the next prime.

84 = 2*2*3*7

Since 7, the largest remaining factor, is prime, we're done.

To write 84 as a product of prime numbers, we need to find prime numbers that can divide evenly into 84. We can start by dividing 84 by the smallest prime number, which is 2.

If we divide 84 by 2, we get 42.

Next, we divide 42 by 2 again, and we get 21.

Now, 21 is an odd number, so 2 cannot divide it evenly. We move on to the next prime number, which is 3.

Dividing 21 by 3, we get 7.

Finally, 7 is a prime number itself, so we cannot divide it any further.

Therefore, we can write 84 as a product of prime numbers as:

84 = 2 * 2 * 3 * 7

To find the prime factorization of 84, we can start by dividing it by the smallest prime number, which is 2.

84 ÷ 2 = 42

Now, we continue dividing the quotient by the smallest prime number until we can no longer divide evenly.

42 ÷ 2 = 21

21 cannot be divided by 2 evenly, so we move on to the next prime number, which is 3.

21 ÷ 3 = 7

7 is a prime number, so we cannot divide it any further.

Therefore, the prime factorization of 84 is:

84 = 2 × 2 × 3 × 7