68.

•  68 is an even number.  

• Divide 68 by 2.

• The remaining quotient is 34.

• 34 is also even.

• Divide 34 by 2.

• The next quotient is 17. 

• 17 is a prime number.

It cannot be divided anymore.34 is also even.

• Divide 34 by 2.

• The next quotient is 17. 

• 17 is a prime number.

It cannot be divided anymore.

Here’s how to find each prime factorization step by step.

A prime factorization means writing a number as a product of only prime numbers.
Prime numbers are numbers greater than 1 that have only two factors: 1 and themselves (like 2, 3, 5, 7, 11, …).

1. Factorize 12

Start with 12.

Since 12 is even, divide by 2:

12/2=6

So far:

12 = 2 x 6

Now factor 6:

6/2=3

So:

6 = 2 x 3

Now 3 is prime, so stop.

Put everything together:

12 = 2 x 2 x 3

Using exponents:

12 = 2^2 x 3

(2 to the second power times 3)

2. Factorize 38

38 is even, so divide by 2:

38/2=19

So:

38 = 2 x 19

19 is prime, so we stop.

Final answer:

38 = 2 x 19

3. Factorize 97

Check whether 97 can be divided by smaller primes:

• not divisible by 2 (it’s odd)

• not divisible by 3 (9 + 7 = 16, not divisible by 3)

• not divisible by 5 (doesn’t end in 0 or 5)

• not divisible by 7

No smaller prime divides it evenly.

So 97 is already prime.

Final answer:

97

4. Factorize 100

100 is even, so divide by 2:

100/2=50

100 = 2 x 50

50 is even:

50/2=25

50 = 2 x 25

25 factors into:

25 = 5 x 5

Put it all together:

100 = 2 x 2 x 5 x 5

Using exponents:

100 = 2^2 x 5^2

(2 to the second power times 5 to the second power)

5. Factorize 184

184 is even:

184/2=92

184 = 2 x 92

92 is even:

92/2=46

92 = 2 x 46

46 is even:

46/2=23

46 = 2 x 23

23 is prime.

Put everything together:

184 = 2 x 2 x 2 x 23

Using exponents:

184 = 2^3 x 23