Final answer:
There are 8 non-prime factors of 2020. To find this, we calculated the total number of factors and subtracted the number of prime factors and 1.
Step-by-step explanation:
The student wants to know how many positive non-prime factors does 2020 have, which is expressed as 2020=22×51×1011 when factored into primes.
To find the number of non-prime factors, we use the formula for finding the total number of factors of a number, which includes prime factors, non-prime factors, and 1. The formula is to add one to each of the exponents of the prime factors and then multiply them together. In this case, (2+1) × (1+1) × (1+1) = 3 × 2 × 2 = 12 total factors.
Since 2020 has three prime factors (2, 5, and 101), we must subtract these, as well as the number 1, to get the number of non-prime factors. So, the total number of non-prime factors is 12 - 4 = 8 non-prime factors.