the number 100 expressed as a product of its prime factors is

The number 100 can be expressed as a product of its prime factors as follows:

1. Start with the number 100.
2. Divide by the smallest prime number, 2: \(100 \div 2 = 50\)
3. Divide 50 by 2: \(50 \div 2 = 25\)
4. Now, 25 is not divisible by 2, so we move to the next prime number, which is 3. \(25\) is not divisible by 3, so we try the next prime number, 5: \(25 \div 5 = 5\)
5. Finally, \(5\) is also a prime number: \(5 \div 5 = 1\)

Putting it all together, we can express 100 as:

\[
100 = 2^2 \times 5^2
\]

So, the prime factorization of 100 is \(2^2 \times 5^2\).