Question

How many factors of 2020 have more than 3 factors? (As an example, 12 has 6 factors, namely 1, 2, 3, 4, 6, and 12.)

Answer 1

To determine the factors of 2020 that have more than three factors, we use the prime factorization of 2020, which is 2² × 5¹ × 101¹. Considering combinations of these prime factors that have at least two different primes, we find that there are 9 factors of 2020 that have more than 3 factors.

Step-by-step explanation:

The student is asking how many factors of the number 2020 have more than three factors themselves. To find the factors of 2020 with more than three factors, we need to first factorize 2020 and then find each divisor's number of factors. The prime factorization of 2020 is 22 × 51 × 1011. A number's factors can be determined by considering all combinations of its prime factors. Numbers with more than 3 factors will have at least two different prime factors. In this case, any combination of the prime factors of 2020 that includes at least two primes will give us a number with more than three factors.

For example, 2, 5, and 101 are factors of 2020, but they have only two factors (1 and themselves) and are not included. However, 10 (2 × 5), 202 (2 × 101), 505 (5 × 101), and 20 (22 × 5) each have more than three factors and are therefore counted. We count such combinations to answer the student's question.

When we perform this count for all factors of 2020, we find that the factors with more than three factors are 4, 5, 10, 20, 101, 202, 505, 1010, and 2020. Therefore, there are 9 factors of 2020 that have more than 3 factors themselves.

Answer 2

`10, 20, 202, 404, 505` and
`1010` has more than
`3` factors.

Step-by-step explanation:

Given: A number
`2020`

To find: How many factors of
`2020` have more than 3 factors?

Solution:

We have,

Factors of
`2020` are
`1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010`

Now, we have to find the number of factors that has more than
`3` factors. So, let us consider each factor of
`2020` one by one.

Factor of
`1: 1`

Factors of
`2: 1, 2`

Factors of
`4: 1, 2, 4`

Factors of
`5: 1, 5`

Factors of
`10: 1, 2, 5, 10`

Factors of
`20: 1, 2,4, 5, 10, 20`

Factors of
`101: 1,101`

Factors of
`202: 1,2, 101, 202`

Factors of
`404: 1, 2, 4, 101, 202, 404`

Factors of
`505: 1, 5, 101, 505`

Factors of
`1010: 1, 2, 5, 10, 101, 202, 505, 1010`

Clearly,
`10, 20, 202, 404, 505` and
`1010` has more than
`3` factors.

Hence,
`10, 20, 202, 404, 505` and
`1010` has more than
`3` factors.