Question

How many of the divisors of 1200 are divisible by 5?​

Answer 1

Ответ:

20

Пошаговое объяснение:

divisors of 1200 - 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200

divisors of 1200 are divisible by (5) - 5, 10, 15, 20, 25, 30, 40, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200

Answer 2

To find the number of divisors of 1200 that are divisible by 5, we need to determine the prime factorization of 1200 and consider the factors that contain at least one factor of 5.

The prime factorization of 1200 is:

1200 = 2^4 * 3 * 5^2

To find the number of divisors, we multiply the exponents of the prime factors incremented by 1 and then multiply the results together. In this case, we have:

Exponent of 2: 4 Exponent of 3: 1 Exponent of 5: 2

The number of divisors of 1200 is calculated as follows:

(4 + 1) * (1 + 1) * (2 + 1) = 5 * 2 * 3 = 30

This means that there are 30 divisors of 1200 in total.

Now, let's determine how many of these divisors are divisible by 5.

Since the factorization contains 5 raised to the power of 2, we have the following options for the factor of 5: 5^0, 5^1, and 5^2. Any divisor that includes a factor of 5^1 or 5^2 will be divisible by 5.

Therefore, the number of divisors of 1200 that are divisible by 5 is:

2 * 3 = 6

So, there are 6 divisors of 1200 that are divisible by 5.