  ### Home > MC1 > Chapter 3 > Lesson 3.3.1 > Problem3-64

3-64.

In Chapter 1, you learned about factors and about prime numbers. It is sometimes useful to represent a number as the product of all of its prime factors. For example, the number $200$  can be factored into primes.

For example, $200 = 2 · 100 = 2 · 2 · 50 = 2 · 2 · 2 · 25 = 2 · 2 · 2 · 5 · 5$ or $200 = 10 · 20 = 2 · 5 · 20 = 2 · 5 · 2 · 10 = 2 · 5 · 2 · 2 · 5$, which gives us the same answer as before written in a different order.

We can then use exponents to write repeated multiplication, showing that the prime factorization of $200$ is $2^3 · 5^2$.

Write the prime factorization of each of the numbers below. Use exponents to represent repeated multiplication.

1.  $100$

Separate the number into all of its primes.
$100=2\left(50\right)$
$=2\left(5\right)\left(10\right)$
$=2\left(50\right)\left(2\right)\left(5\right)$

Use exponents to simplify the repeated multiplication.

$2^2(5^2)$

$2^2(5^2) = 100$

1.  $36$

Follow the steps outlined in part (a). Remember to use exponents!

$2^2(3^2)$

1.  $54$

Follow the steps outlined in part (a). Check your work to make sure the product of the prime factors is $54$.

1.  $400$

Follow the steps outlined in part (a). It may also be helpful to think about how $400$ relates to $100$, and then use your answer from part (a) as a starting point.