I'm home schooling my son and i cant figure out what the factorization of 68 is

Let's see which numbers go evenly into 68.

2 * 34
4 * 17

That's it.

Factors are numbers that you can multiply together to get the number. for example, 1 and 68, 2 and 34, etc. All of these numbers are factors of 68.

Excuse the political intrusion, but how can you justify home-schooling if you as the instructor cannot perform a simple arithmetic operation such as factoring the number 68

I wondered the same thing, Reiny. I also Googled factoring to make sure that I was right -- and found several excellent sites that explain factoring.

To find the factorization of 68, we need to determine all the numbers that divide evenly into 68 without leaving a remainder. One way to do this is by attempting to divide 68 by smaller numbers and checking if there is no remainder. We start with the number 1 and gradually increase it.

Let's go step-by-step:

1. Begin by dividing 68 by the smallest whole number, which is 1.
- 68 ÷ 1 = 68 (no remainder)

2. Next, divide 68 by 2.
- 68 ÷ 2 = 34 (no remainder)

3. Continue dividing 68 by the next whole number, which is 3.
- 68 ÷ 3 = 22.666...

Since dividing by 3 does not result in a whole number, it is not a factor of 68.

4. Now, try dividing 68 by 4.
- 68 ÷ 4 = 17 (no remainder)

5. Try 68 divided by 5.
- 68 ÷ 5 = 13.6...

Dividing by 5 does not yield a whole number, so it is not a factor of 68.

6. Let's move on to dividing 68 by 6.
- 68 ÷ 6 = 11.333...

Again, dividing by 6 does not yield a whole number.

7. Try dividing 68 by 7.
- 68 ÷ 7 = 9.714...

Dividing by 7 does not give us a whole number.

8. Lastly, divide 68 by 8.
- 68 ÷ 8 = 8.5

Dividing by 8 does not result in a whole number either.

So, the factors of 68 are 1, 2, 4, 17, 34, and 68. The factorization of 68 is 2 × 2 × 17, which can be written as 2² × 17.