Have you ever wondered what makes up a number, not just in terms of addition or subtraction, but its fundamental, indivisible components? It's a bit like looking at a complex LEGO structure and wanting to know exactly which individual bricks were used to build it. Today, we're going to do just that with the number 104.
Think of prime numbers as the alphabet of mathematics. They are numbers greater than 1 that can only be divided evenly by 1 and themselves. Numbers like 2, 3, 5, 7, 11, and so on. When we talk about expressing a number as a product of its prime factors, we're essentially breaking it down into its smallest, most basic multiplicative pieces.
So, how do we find these prime building blocks for 104? It's a systematic process, and it's quite satisfying when you see it all come together. We start by looking for the smallest prime number that divides 104. That's 2, right? Because 104 is an even number.
104 divided by 2 gives us 52. Now, we take 52 and ask the same question: what's the smallest prime number that divides it? Again, it's 2. So, 52 divided by 2 is 26.
We're not done yet. We look at 26. Is it divisible by 2? Yes, it is! 26 divided by 2 equals 13.
Now we're left with 13. Here's where we pause. Is 13 divisible by any prime number other than 1 and itself? No, it's not. 13 is a prime number. This means we've reached the end of our factorization journey for 104.
Putting it all together, we found that 104 can be expressed as the product of 2, 2, 2, and 13. In mathematical shorthand, we often write this using exponents to show how many times a prime factor appears. So, 104 is equal to 2 multiplied by itself three times (which we write as 2³), and then multiplied by 13.
Therefore, 104 as a product of its prime factors is 2³ × 13. It's a neat way to see the unique mathematical fingerprint of a number, built from its most fundamental parts.