what is the number of factors of the product 126*216?
Well, let's calculate it in a "factor-ious" way!
First, let's break down 126 into prime factors. It can be written as 2 * 3^2 * 7.
Now, let's break down 216 into prime factors. It can be written as 2^3 * 3^3.
To find the factors of their product, we need to multiply the powers of all the prime factors together. In this case, we have 2^4 * 3^5 * 7^1.
Now, to find the number of factors, we need to take the exponent of each prime factor and add one. So, we have (4+1) * (5+1) * (1+1) = 5 * 6 * 2 = 60 factors!
Isn't it "factor-tastic"?