CPM Homework Help : MC1 Problem 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.

$100$
Step 1(a):
Separate the number into all of its primes.
$100=2\left(50\right)$
$=2\left(5\right)\left(10\right)$
$=2\left(50\right)\left(2\right)\left(5\right)$
Step 2(a):
Use exponents to simplify the repeated multiplication.
$2^2(5^2)$
Answer (a):
$2^2(5^2) = 100$

$36$
Hint (b):
Follow the steps outlined in part (a). Remember to use exponents!
Answer (b):
$2^2(3^2)$

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

$400$
Hint (d):
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.