Question

A number is written with the following factorization: 2^2 × 3 × 5^4 × 11^2. Is this factorization a prime factorization? Explain why or why not. If it is not correct, give the correct prime factorization of the number.

Answer 1

It is a prime factorization because each base (2,3,5, and 11) is a prime number.

A prime number is one where the only factors of it are 1 and itself.

• factors of 2 = 1 and 2
• factors of 3 = 1 and 3
• factors of 5 = 1 and 5
• factors of 11 = 1 and 11

Instead of saying something like 11^2, we could write 11*11. Similarly, 5^4 could be written as 5*5*5*5. Though it's a good idea to use exponents so you make the prime factorization more compact and save time.

The '3' without an exponent is the same as 3^1. You'll often see that exponent of 1 left out. Again this is to save time.