To find the number of factors of 1440 that are divisible by 5, we need to follow these steps:

1. **Prime Factorization of 1440**:
First, we find the prime factorization of 1440.
$$
1440 = 2^5 \times 3^2 \times 5
$$

2. **Factors of 1440**:
The factors of 1440 are all the numbers that can be formed by multiplying the prime factors in various combinations.

3. **Factors Divisible by 5**:
To be divisible by 5, a factor must include at least one 5 in its prime factorization. Therefore, we consider the factors of the form:
$$
5 \times (2^a \times 3^b)
$$
where $a$ can be 0, 1, 2, 3, 4, or 5 (6 choices), and $b$ can be 0, 1, or 2 (3 choices).

4. **Counting the Factors**:
The total number of such factors is the product of the number of choices for $a$ and $b$:
$$
6 \times 3 = 18
$$

Therefore, the number of factors of 1440 that are divisible by 5 is $18$.

Question

To find the number of factors of 1440 that are divisible by 5, we need to follow these steps:

1. **Prime Factorization of 1440**:
   First, we find the prime factorization of 1440.
   $$
   1440 = 2^5 \times 3^2 \times 5
   $$

2. **Factors of 1440**:
   The factors of 1440 are all the numbers that can be formed by multiplying the prime factors in various combinations.

3. **Factors Divisible by 5**:
   To be divisible by 5, a factor must include at least one 5 in its prime factorization. Therefore, we consider the factors of the form:
   $$
   5 \times (2^a \times 3^b)
   $$
   where $a$ can be 0, 1, 2, 3, 4, or 5 (6 choices), and $b$ can be 0, 1, or 2 (3 choices).

4. **Counting the Factors**:
   The total number of such factors is the product of the number of choices for $a$ and $b$:
   $$
   6 \times 3 = 18
   $$

Therefore, the number of factors of 1440 that are divisible by 5 is $18$.

Knowee AI · Accepted Answer

To find the number of factors of 1440 that are divisible by 5, we need to follow these steps:

1. **Prime Factorization of 1440**:
   First, we find the prime factorization of 1440.
   $$
   1440 = 2^5 \times 3^2 \times 5
   $$

2. **Factors of 1440**:
   The factors of 1440 are all the numbers that can be formed by multiplying the prime factors in various combinations.

3. **Factors Divisible by 5**:
   To be divisible by 5, a factor must include at least one 5 in its prime factorization. Therefore, we consider the factors of the form:
   $$
   5 \times (2^a \times 3^b)
   $$
   where $a$ can be 0, 1, 2, 3, 4, or 5 (6 choices), and $b$ can be 0, 1, or 2 (3 choices).

4. **Counting the Factors**:
   The total number of such factors is the product of the number of choices for $a$ and $b$:
   $$
   6 \times 3 = 18
   $$

Therefore, the number of factors of 1440 that are divisible by 5 is $18$.

For the number 1440, find the number of factors which are divisible by 5.12141618None of the above

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