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Rule about factorials greater than or equal to 5!

A) They are always prime.
B) They are divisible by 5.
C) They have no factors.
D) They are even.

User Stryner
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1 Answer

1 vote

Final answer:

Factorials greater than or equal to 5! are always divisible by 5 because they include the multiplication of all integers up to at least 5, and therefore 5 is a factor.

Step-by-step explanation:

The question deals with properties of factorials for numbers greater than or equal to 5! (5 factorial). The correct answer is B) They are divisible by 5. This is because the factorial of a number is the product of all positive integers up to that number. For example, 5! = 5 × 4 × 3 × 2 × 1. Since the number 5 is included in the multiplication for 5! and all greater factorials, it ensures that these numbers will always be divisible by 5. In addition, these numbers will not be prime (since they have more factors than just 1 and themselves), they will indeed have many factors, and they will also always be even because they include the multiplication of at least one 2 and one number greater than 2, which guarantees an even product.

User Bilwit
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