   SEARCH HOME Math Central Quandaries & Queries  Question from michelle, a parent: how would you write this: factor 48 as a product of primes written in exponential form Hi Michelle.

Any positive integer can be written as a unique product of prime numbers.

For example, to break 540 down to its prime factors, I simply start dividing by prime numbers:

• 540 is even, so 2 goes into it: 540 / 2 = 270.
• 270 is even, so 2 goes into it: 270 / 2 = 135.
• 3 goes into 135 (because 1+3+5=9 and 3 goes into 9), so 135 / 3 = 45.
• 5 goes into 45, so 45 / 5 = 9.
• 3 goes into 9, so 9 / 3 = 3.
• 3 goes into itself, so 3 / 3 = 1. When I get to 1, I stop.

Now I list what I divided by: 2, 2, 3, 5, 3, 3. When I multiply all these together I will get the original number:

2 × 2 × 3 × 5 × 3 × 3 = 540.

To write this in exponential form, I just re-order it to group the prime numbers together:

2 × 2 × 3 × 3 × 3 × 5

And then count the number of times each factor appears:

22 × 33 × 51.

Usually, when an exponent is 1, we don't write it because it is assumed, so our final answer is:

22 × 33 × 5.

Now you try it by breaking down 48 into its prime factors, Michelle.

Cheers,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.